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Wyświetlanie 1-15 z 68
Tytuł:
Degree Sum Condition for the Existence of Spanning k-Trees in Star-Free Graphs
Autorzy:
Furuya, Michitaka
Maezawa, Shun-ichi
Matsubara, Ryota
Matsuda, Haruhide
Tsuchiya, Shoichi
Yashima, Takamasa
Powiązania:
https://bibliotekanauki.pl/articles/32361756.pdf
Data publikacji:
2022-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
spanning tree
k -tree
star-free
degree sum condition
Opis:
For an integer k ≥ 2, a k-tree T is defined as a tree with maximum degree at most k. If a k-tree T spans a graph G, then T is called a spanning k-tree of G. Since a spanning 2-tree is a Hamiltonian path, a spanning k-tree is an extended concept of a Hamiltonian path. The first result, implying the existence of k-trees in star-free graphs, was by Caro, Krasikov, and Roditty in 1985, and independently, Jackson and Wormald in 1990, who proved that for any integer k with k ≥ 3, every connected K1,k-free graph contains a spanning k-tree. In this paper, we focus on a sharp condition that guarantees the existence of a spanning k-tree in K1,k+1-free graphs. In particular, we show that every connected K1,k+1-free graph G has a spanning k-tree if the degree sum of any 3k−3 independent vertices in G is at least |G|−2, where |G| is the order of G.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 1; 5-13
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Describing Minor 5-Stars in 3-Polytopes with Minimum Degree 5 and No Vertices of Degree 6 or 7
Autorzy:
Batueva, Ts.Ch-D.
Borodin, O.V.
Ivanova, A.O.
Nikiforov, D.V.
Powiązania:
https://bibliotekanauki.pl/articles/32361718.pdf
Data publikacji:
2022-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
planar graph
structural properties
3-polytope
5-star
neighborhood
Opis:
In 1940, in attempts to solve the Four Color Problem, Henry Lebesgue gave an approximate description of the neighborhoods of 5-vertices in the class P5 of 3-polytopes with minimum degree 5. This description depends on 32 main parameters. (6, 6, 7, 7, 7), (6, 6, 6, 7, 9), (6, 6, 6, 6, 11), (5, 6, 7, 7, 8), (5, 6, 6, 7, 12), (5, 6, 6, 8, 10), (5, 6, 6, 6, 17), (5, 5, 7, 7, 13), (5, 5, 7, 8, 10), (5, 5, 6, 7, 27), (5, 5, 6, 6, ∞), (5, 5, 6, 8, 15), (5, 5, 6, 9, 11), (5, 5, 5, 7, 41), (5, 5, 5, 8, 23), (5, 5, 5, 9, 17), (5, 5, 5, 10, 14), (5, 5, 5, 11, 13) Not many precise upper bounds on these parameters have been obtained as yet, even for restricted subclasses in P5. In 2018, Borodin, Ivanova, Kazak proved that every forbidding vertices of degree from 7 to 11 results in a tight description (5, 5, 6, 6, ∞), (5, 6, 6, 6, 15), (6, 6, 6, 6, 6). Recently, Borodin, Ivanova, and Kazak proved every 3-polytope in P5 with no vertices of degrees 6, 7, and 8 has a 5-vertex whose neighborhood is majorized by one of the sequences (5, 5, 5, 5, ∞) and (5, 5, 10, 5, 12), which is tight and improves a corresponding description (5, 5, 5, 5, ∞), (5, 5, 9, 5, 17), (5, 5, 10, 5, 14), (5, 5, 11, 5, 13) that follows from the Lebesgue Theorem. The purpose of this paper is to prove that every 3-polytope with minimum degree 5 and no vertices of degree 6 or 7 has a 5-vertex whose neighborhood is majorized by one of the ordered sequences (5, 5, 5, 5, ∞), (5, 5, 8, 5, 14), or (5, 5, 10, 5, 12).
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 2; 535-548
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some Properties of the Eigenvalues of the Net Laplacian Matrix of a Signed Graph
Autorzy:
Stanić, Zoran
Powiązania:
https://bibliotekanauki.pl/articles/32304147.pdf
Data publikacji:
2022-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
(net) Laplacian matrix
edge perturbations
largest eigenvalue
net-degree
Opis:
Given a signed graph $ \dot{G} $, let $ A_{ \dot{G} } $ and $ D_{\dot{G}}^\pm $ denote its standard adjacency matrix and the diagonal matrix of vertex net-degrees, respectively. The net Laplacian matrix of $ \dot{G} $ is defined to be $ N_{ \dot{G} } = D_{\dot{G}}^\pm - A_{ \dot{G} } $. In this study we give some properties of the eigenvalues of $ N_{ \dot{G} } $. In particular, we consider their behaviour under some edge perturbations, establish some relations between them and the eigenvalues of the standard Laplacian matrix and give some lower and upper bounds for the largest eigenvalue of $ N_{ \dot{G} } $.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 3; 893-903
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Trees Whose Even-Degree Vertices Induce a Path are Antimagic
Autorzy:
Lozano, Antoni
Mora, Mercè
Seara, Carlos
Tey, Joaquín
Powiązania:
https://bibliotekanauki.pl/articles/32304141.pdf
Data publikacji:
2022-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
antimagic labeling
tree
Opis:
An antimagic labeling of a connected graph G is a bijection from the set of edges E(G) to {1, 2, . . ., |E(G)|} such that all vertex sums are pairwise distinct, where the vertex sum at vertex v is the sum of the labels assigned to edges incident to v. A graph is called antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that every simple connected graph other than K2 is antimagic; however the conjecture remains open, even for trees. In this note we prove that trees whose vertices of even degree induce a path are antimagic, extending a result given by Liang, Wong, and Zhu [Anti-magic labeling of trees, Discrete Math. 331 (2014) 9–14].
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 3; 959-966
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Distribution of Contractible Edges and the Structure of Noncontractible Edges having Endvertices with Large Degree in a 4-Connected Graph
Autorzy:
Nakamura, Shunsuke
Powiązania:
https://bibliotekanauki.pl/articles/32323873.pdf
Data publikacji:
2021-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
4-connected graph
contractible edge
cross free
Opis:
Let G be a 4-connected graph G, and let Ec(G) denote the set of 4-contractible edges of G. We prove results concerning the distribution of edges in Ec(G). Roughly speaking, we show that there exists a set K0 and a mapping φ : K0 → Ec(G) such that |φ-1(e)| ≤ 4 for each e ∈ Ec(G).
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 4; 1051-1066
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Domination Number of Graphs with Minimum Degree Five
Autorzy:
Bujtás, Csilla
Powiązania:
https://bibliotekanauki.pl/articles/32222697.pdf
Data publikacji:
2021-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
dominating set
domination number
discharging method
Opis:
We prove that for every graph G on n vertices and with minimum degree five, the domination number γ(G) cannot exceed n/3. The proof combines an algorithmic approach and the discharging method. Using the same technique, we provide a shorter proof for the known upper bound 4n/11 on the domination number of graphs of minimum degree four.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 3; 763-777
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Linear List Coloring of Some Sparse Graphs
Autorzy:
Chen, Ming
Li, Yusheng
Zhang, Li
Powiązania:
https://bibliotekanauki.pl/articles/32083756.pdf
Data publikacji:
2021-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
linear coloring
maximum average degree
planar graphs
discharging
Opis:
A linear $k$-coloring of a graph is a proper $k$-coloring of the graph such that any subgraph induced by the vertices of any pair of color classes is a union of vertex-disjoint paths. A graph $G$ is linearly $L$-colorable if there is a linear coloring $c$ of $G$ for a given list assignment $L = \{L(v) : v ∈ V(G)\}$ such that $c(v) ∈ L(v)$ for all $v ∈ V(G)$, and $G$ is linearly $k$-choosable if $G$ is linearly $L$-colorable for any list assignment with $|L(v)| ≥ k$. The smallest integer $k$ such that $G$ is linearly $k$-choosable is called the linear list chromatic number, denoted by $lc_l(G)$. It is clear that \(lc_l(G)≥\Big\lceil\frac{\Delta(G)}{1}\Big\rceil+1\) for any graph $G$ with maximum degree $\Delta(G)$. The maximum average degree of a graph $G$, denoted by $mad(G)$, is the maximum of the average degrees of all subgraphs of $G$. In this note, we shall prove the following. Let $G$ be a graph, (1) if $mad(G)<\frac{8}{3}$ and $\Delta(G) ≥ 7$, then \(lc_l(G)=\Big\lceil\frac{\Delta(G)}{2}\Big\rceil+1\); (2) if $mad(G)<{18}{7}$ and $\Delta(G) ≥ 5$, then \(lc_l(G)=\Big\lceil\frac{\Delta(G)}{2}\Big\rceil+1\); (3) if $mad(G)<{20}{7}$ and $\Delta(G) ≥ 5$, then \(lc_l(G)≤\Big\lceil\frac{\Delta(G)}{2}\Big\rceil+2\).
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 1; 51-64
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Neighbor Product Distinguishing Total Colorings of Planar Graphs with Maximum Degree at least Ten
Autorzy:
Dong, Aijun
Li, Tong
Powiązania:
https://bibliotekanauki.pl/articles/32227944.pdf
Data publikacji:
2021-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
total coloring
neighbor product distinguishing coloring
planar graph
Opis:
A proper [k]-total coloring c of a graph G is a proper total coloring c of G using colors of the set [k] = {1, 2, . . ., k}. Let p(u) denote the product of the color on a vertex u and colors on all the edges incident with u. For each edge uv ∈ E(G), if p(u) ≠ p(v), then we say the coloring c distinguishes adjacent vertices by product and call it a neighbor product distinguishing k-total coloring of G. By X″∏(G), we denote the smallest value of k in such a coloring of G. It has been conjectured by Li et al. that Δ(G) + 3 colors enable the existence of a neighbor product distinguishing total coloring. In this paper, by applying the Combinatorial Nullstellensatz, we obtain that the conjecture holds for planar graph with Δ(G) ≥ 10. Moreover, for planar graph G with Δ(G) ≥ 11, it is neighbor product distinguishing (Δ(G) + 2)-total colorable, and the upper bound Δ(G) + 2 is tight.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 4; 981-999
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Implicit Heavy Subgraphs and Hamiltonicity of 2-Connected Graphs
Autorzy:
Zheng, Wei
Wideł, Wojciech
Wang, Ligong
Powiązania:
https://bibliotekanauki.pl/articles/32083821.pdf
Data publikacji:
2021-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
implicit degree
implicit o-heavy
implicit f-heavy
implicit c-heavy
Hamilton cycle
Opis:
A graph G of order n is implicit claw-heavy if in every induced copy of K1,3 in G there are two non-adjacent vertices with sum of their implicit degrees at least n. We study various implicit degree conditions (including, but not limiting to, Ore- and Fan-type conditions) imposing of which on specific induced subgraphs of a 2-connected implicit claw-heavy graph ensures its Hamiltonicity. In particular, we improve a recent result of [X. Huang, Implicit degree condition for Hamiltonicity of 2-heavy graphs, Discrete Appl. Math. 219 (2017) 126–131] and complete the characterizations of pairs of o-heavy and f-heavy subgraphs for Hamiltonicity of 2-connected graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 1; 167-181
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
2-Connected Hamiltonian Claw-Free Graphs Involving Degree Sum of Adjacent Vertices
Autorzy:
Tian, Tao
Xiong, Liming
Powiązania:
https://bibliotekanauki.pl/articles/32034090.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Hamiltonian cycle
degree sum
dominating closed trail
closure
Opis:
For a graph H, define $\overline{\sigma}_2(H)=min\{d(u)+d(v)|uv∈E(H)\}$. Let $H$ be a 2-connected claw-free simple graph of order $n$ with \(\delta(H) ≥ 3\). In [J. Graph Theory 86 (2017) 193–212], Chen proved that if $\overline{\sigma}_2(H)≥\frac{n}{2}−1$ and $n$ is sufficiently large, then $H$ is Hamiltonian with two families of exceptions. In this paper, we refine the result. We focus on the condition $\overline{\sigma}_2(H)≥\frac{2n}{5}−1$, and characterize non-Hamiltonian 2-connected claw-free graphs $H$ of order $n$ sufficiently large with $\overline{\sigma}_2(H)≥\frac{2n}{5}−1$. As byproducts, we prove that there are exactly six graphs in the family of 2-edge-connected triangle-free graphs of order at most seven that have no spanning closed trail and give an improvement of a result of Veldman in [Discrete Math. 124 (1994) 229–239].
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 85-106
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Eccentricity of Networks with Structural Constraints
Autorzy:
Krnc, Matjaž
Sereni, Jean-Sébastien
Škrekovski, Riste
Yilma, Zelealem B.
Powiązania:
https://bibliotekanauki.pl/articles/31348091.pdf
Data publikacji:
2020-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
eccentricity
network
bipartite graph
complex network
maximum degree
Opis:
The eccentricity of a node v in a network is the maximum distance from v to any other node. In social networks, the reciprocal of eccentricity is used as a measure of the importance of a node within a network. The associated centralization measure then calculates the degree to which a network is dominated by a particular node. In this work, we determine the maximum value of eccentricity centralization as well as the most centralized networks for various classes of networks including the families of bipartite networks (two-mode data) with given partition sizes and tree networks with fixed number of nodes and fixed maximum degree. To this end, we introduce and study a new way of enumerating the nodes of a tree which might be of independent interest.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 4; 1141-1162
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Equating κ Maximum Degrees in Graphs without Short Cycles
Autorzy:
Fürst, Maximilian
Gentner, Michael
Jäger, Simon
Rautenbach, Dieter
Henning, Michael A.
Powiązania:
https://bibliotekanauki.pl/articles/31523205.pdf
Data publikacji:
2020-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
maximum degree
repeated degrees
repetition number
Opis:
For an integer $k$ at least 2, and a graph $G$, let $f_k(G)$ be the minimum cardinality of a set $X$ of vertices of $G$ such that $G − X$ has either $k$ vertices of maximum degree or order less than $k$. Caro and Yuster [Discrete Mathematics 310 (2010) 742–747] conjectured that, for every $k$, there is a constant $c_k$ such that \(f_k(G)≤c_k\sqrt{n(G)}\) for every graph $G$. Verifying a conjecture of Caro, Lauri, and Zarb [arXiv:1704.08472v1], we show the best possible result that, if t is a positive integer, and $F$ is a forest of order at most \(1/6(t^3+6t^2+17t+12)\), then $f_2(F) ≤ t$. We study $f_3(F)$ for forests $F$ in more detail obtaining similar almost tight results, and we establish upper bounds on $f_k(G)$ for graphs $G$ of girth at least 5. For graphs $G$ of girth more than $2p$, for $p$ at least 3, our results imply \(f_k(G)=O\bigg(n(G)\frac{p+1}{3_p}\bigg)\). Finally, we show that, for every fixed $k$, and every given forest $F$, the value of $f_k(F)$ can be determined in polynomial time.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 3; 841-853
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of Regular Nut Graphs for Degree at Most 11
Autorzy:
Fowler, Patrick W.
Gauci, John Baptist
Goedgebeur, Jan
Pisanski, Tomaž
Sciriha, Irene
Powiązania:
https://bibliotekanauki.pl/articles/31550028.pdf
Data publikacji:
2020-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
nut graph
core graph
regular graph
nullity
Opis:
A nut graph is a singular graph with one-dimensional kernel and corresponding eigenvector with no zero elements. The problem of determining the orders n for which d-regular nut graphs exist was recently posed by Gauci, Pisanski and Sciriha. These orders are known for d ≤ 4. Here we solve the problem for all remaining cases d ≤ 11 and determine the complete lists of all d-regular nut graphs of order n for small values of d and n. The existence or non-existence of small regular nut graphs is determined by a computer search. The main tool is a construction that produces, for any d-regular nut graph of order n, another d-regular nut graph of order n+2d. If we are given a sufficient number of d-regular nut graphs of consecutive orders, called seed graphs, this construction may be applied in such a way that the existence of all d-regular nut graphs of higher orders is established. For even d the orders n are indeed consecutive, while for odd d the orders n are consecutive even numbers. Furthermore, necessary conditions for combinations of order and degree for vertex-transitive nut graphs are derived.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 2; 533-557
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Incidence Coloring—Cold Cases
Autorzy:
Kardoš, František
Maceková, Mária
Mockovčiaková, Martina
Sopena, Éric
Soták, Roman
Powiązania:
https://bibliotekanauki.pl/articles/32083735.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
incidence coloring
incidence chromatic number
planar graph
maximum average degree
Opis:
An incidence in a graph G is a pair (v, e) where v is a vertex of G and e is an edge of G incident to v. Two incidences (v, e) and (u, f) are adjacent if at least one of the following holds: (i) v = u, (ii) e = f, or (iii) edge vu is from the set {e, f}. An incidence coloring of G is a coloring of its incidences assigning distinct colors to adjacent incidences. The minimum number of colors needed for incidence coloring of a graph is called the incidence chromatic number. It was proved that at most Δ(G) + 5 colors are enough for an incidence coloring of any planar graph G except for Δ(G) = 6, in which case at most 12 colors are needed. It is also known that every planar graph G with girth at least 6 and Δ(G) ≥ 5 has incidence chromatic number at most Δ(G) + 2. In this paper we present some results on graphs regarding their maximum degree and maximum average degree. We improve the bound for planar graphs with Δ(G) = 6. We show that the incidence chromatic number is at most Δ(G) + 2 for any graph G with mad(G) < 3 and Δ(G) = 4, and for any graph with mad(G)<103 and Δ(G) ≥ 8.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 345-354
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Light Minor 5-Stars in 3-Polytopes with Minimum Degree 5 and No 6-Vertices
Autorzy:
Borodin, Oleg V.
Ivanova, Anna O.
Vasil’eva, Ekaterina I.
Powiązania:
https://bibliotekanauki.pl/articles/31348169.pdf
Data publikacji:
2020-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
planar map
planar graph
3-polytope
structural properties
5-star
weight
height
Opis:
In 1940, Lebesgue gave an approximate description of the neighborhoods of 5-vertices in the class P5 of 3-polytopes with minimum degree 5. Given a 3-polytope P, by w(P) denote the minimum of the degree-sum (weight) of the neighborhoods of 5-vertices (minor 5-stars) in P. In 1996, Jendrol’ and Madaras showed that if a polytope P in P5 is allowed to have a 5-vertex adjacent to four 5-vertices, then w(P) can be arbitrarily large. For each P in P5 without vertices of degree 6 and 5-vertices adjacent to four 5-vertices, it follows from Lebesgue’s Theorem that w(P) ≤ 68. Recently, this bound was lowered to w(P) ≤ 55 by Borodin, Ivanova, and Jensen and then to w(P) ≤ 51 by Borodin and Ivanova. In this note, we prove that every such polytope P satisfies w(P) ≤ 44, which bound is sharp.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 4; 985-994
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 68

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