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Wyświetlanie 1-15 z 29
Tytuł:
Further Results on Packing Related Parameters in Graphs
Autorzy:
Mojdeh, Doost Ali
Samadi, Babak
Yero, Ismael G.
Powiązania:
https://bibliotekanauki.pl/articles/32361731.pdf
Data publikacji:
2022-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
packing number
open packing number
independence number
Nordhaus-Gaddum inequality
total domination number
Opis:
Given a graph G = (V, E), a set B ⊆ V (G) is a packing in G if the closed neighborhoods of every pair of distinct vertices in B are pairwise disjoint. The packing number ρ(G) of G is the maximum cardinality of a packing in G. Similarly, open packing sets and open packing number are defined for a graph G by using open neighborhoods instead of closed ones. We give several results concerning the (open) packing number of graphs in this paper. For instance, several bounds on these packing parameters along with some Nordhaus-Gaddum inequalities are given. We characterize all graphs with equal packing and independence numbers and give the characterization of all graphs for which the packing number is equal to the independence number minus one. In addition, due to the close connection between the open packing and total domination numbers, we prove a new upper bound on the total domination number γt(T) for a tree T of order n ≥ 2 improving the upper bound γt(T) ≤ (n + s)/2 given by Chellali and Haynes in 2004, in which s is the number of support vertices of T.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 2; 333-348
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
New Results Relating Independence and Matchings
Autorzy:
Caro, Yair
Davila, Randy
Pepper, Ryan
Powiązania:
https://bibliotekanauki.pl/articles/32304143.pdf
Data publikacji:
2022-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
independent sets
independence number
matchings
matching number
Opis:
In this paper we study relationships between the matching number, written µ(G), and the independence number, written α(G). Our first main result is to show α(G) ≤ µ(G) + |X| − µ(G[NG[X]]), where X is any intersection of maximum independent sets in G. Our second main result is to show δ(G) α(G) ≤ Δ(G)µ(G), where δ(G) and Δ(G) denote the minimum and maximum vertex degrees of G, respectively. These results improve on and generalize known relations between µ(G) and α(G). Further, we also give examples showing these improvements.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 3; 921-935
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Domination Number, Independent Domination Number and 2-Independence Number in Trees
Autorzy:
Dehgardi, Nasrin
Sheikholeslami, Seyed Mahmoud
Valinavaz, Mina
Aram, Hamideh
Volkmann, Lutz
Powiązania:
https://bibliotekanauki.pl/articles/32083746.pdf
Data publikacji:
2021-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
2-independence number
domination number
independent domination number
Opis:
For a graph $G$, let $\gamma(G)$ be the domination number, $i(G)$ be the independent domination number and $\beta_2(G)$ be the 2-independence number. In this paper, we prove that for any tree $T$ of order $n ≥ 2, 4\beta_2(T) − 3\gamma(T) ≥ 3i(T)$, and we characterize all trees attaining equality. Also we prove that for every tree $T$ of order \(n ≥ 2, i(T)≤\frac{3\beta_2(T)}{4}\), and we characterize all extreme trees.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 1; 39-49
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Independence Number and Packing Coloring of Generalized Mycielski Graphs
Autorzy:
Bidine, Ez Zobair
Gadi, Taoufiq
Kchikech, Mustapha
Powiązania:
https://bibliotekanauki.pl/articles/32222704.pdf
Data publikacji:
2021-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
independence number
packing chromatic number
Mycielskians
generalized Mycielskians
Opis:
For a positive integer k ⩾ 1, a graph G with vertex set V is said to be k-packing colorable if there exists a mapping f : V ↦ {1, 2, . . ., k} such that any two distinct vertices x and y with the same color f(x) = f(y) are at distance at least f(x) + 1. The packing chromatic number of a graph G, denoted by χρ(G), is the smallest integer k such that G is k-packing colorable. In this work, we study both independence and packing colorings in the m-generalized Mycielskian of a graph G, denoted μm(G). We first give an explicit formula for α (μm(G)) when m is odd and bounds when m is even. We then use these results to give exact values of α(μm(Kn)) for any m and n. Next, we give bounds on the packing chromatic number, χρ, of μm(G). We also prove the existence of large planar graphs whose packing chromatic number is 4. The rest of the paper is focused on packing chromatic numbers of the Mycielskian of paths and cycles.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 3; 725-747
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Independent Transversal Total Domination versus Total Domination in Trees
Autorzy:
Martínez, Abel Cabrera
Peterin, Iztok
Yero, Ismael G.
Powiązania:
https://bibliotekanauki.pl/articles/32083825.pdf
Data publikacji:
2021-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
independent transversal total domination number
total domination number
independence number
trees
Opis:
A subset of vertices in a graph G is a total dominating set if every vertex in G is adjacent to at least one vertex in this subset. The total domination number of G is the minimum cardinality of any total dominating set in G and is denoted by γt(G). A total dominating set of G having nonempty intersection with all the independent sets of maximum cardinality in G is an independent transversal total dominating set. The minimum cardinality of any independent transversal total dominating set is denoted by γtt(G). Based on the fact that for any tree T, γt(T) ≤ γtt(T) ≤ γt(T) + 1, in this work we give several relationships between γtt(T) and γt(T) for trees T which are leading to classify the trees which are satisfying the equality in these bounds.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 1; 213-224
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Independence Number, Connectivity and All Fractional (a, b, k)-Critical Graphs
Autorzy:
Yuan, Yuan
Hao, Rong-Xia
Powiązania:
https://bibliotekanauki.pl/articles/31343586.pdf
Data publikacji:
2019-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
independence number
connectivity
fractional [a
b]-factor
frac- tional (a
b
k)-critical graph
all fractional (a
Opis:
Let $G$ be a graph and $a$, $b$ and $k$ be nonnegative integers with $ 1 \le a \le b $. A graph $G$ is defined as all fractional $(a, b, k)$-critical if after deleting any $k$ vertices of $G$, the remaining graph has all fractional $[a, b]$-factors. In this paper, we prove that if \( \kappa(G) \ge \text{max} \{ \tfrac{(b+1)^2+2k}{2}, \tfrac{(b+1)^2 \alpha(G)+4ak}{4a} \} \), then $G$ is all fractional $(a, b, k)$-critical. If $k = 0$, we improve the result given in [Filomat 29 (2015) 757-761]. Moreover, we show that this result is best possible in some sense.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 1; 183-190
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
New Formulae for the Decycling Number of Graphs
Autorzy:
Yang, Chao
Ren, Han
Powiązania:
https://bibliotekanauki.pl/articles/31343660.pdf
Data publikacji:
2019-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
decycling number
independence number
cycle rank
margin number
Opis:
A set $S$ of vertices of a graph $G$ is called a decycling set if $G−S$ is acyclic. The minimum order of a decycling set is called the decycling number of $G$, and denoted by $ \nabla(G)$. Our results include: (a) For any graph $G$, $ \nabla (G) = n - \max_T \{ \alpha (G- E(T)) \} $, where $T$ is taken over all the spanning trees of $G$ and $ \alpha (G − E(T)) $ is the independence number of the co-tree $ G − E(T) $. This formula implies that computing the decycling number of a graph $G$ is equivalent to finding a spanning tree in $G$ such that its co-tree has the largest independence number. Applying the formula, the lower bounds for the decycling number of some (dense) graphs may be obtained. (b) For any decycling set $S$ of a $k$-regular graph $G$, $ |S| = \frac{1}{k-1} (\beta (G) + m(S)) $, where $ \beta(G) = |E(G)|−|V (G)|+1 $ and $ m(S) = c+|E(S)|−1$, $c$ and $|E(S)|$ are, respectively, the number of components of $G − S$ and the number of edges in $G[S]$. Hence $S$ is a $ \nabla$-set if and only if $m(S)$ is minimum, where $ \nabla$-set denotes a decycling set containing exactly $ \nabla(G)$ vertices of $G$. This provides a new way to locate $ \nabla(G) $ for $k$-regular graphs $G$. (c) 4-regular graphs $G$ with the decycling number $ \nabla (G) = \ceil{ \tfrac{ \beta(G)}{3} } $ are determined.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 1; 125-141
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On 3-Colorings of Direct Products of Graphs
Autorzy:
Špacapan, Simon
Powiązania:
https://bibliotekanauki.pl/articles/31343446.pdf
Data publikacji:
2019-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
independence number
direct product
Hedetniemi’s conjecture
Opis:
The k-independence number of a graph G, denoted as αk(G), is the order of a largest induced k-colorable subgraph of G. In [S. Špacapan, The k-independence number of direct products of graphs, European J. Combin. 32 (2011) 1377–1383] the author conjectured that the direct product G × H of graphs G and H obeys the following bound αk(G×H)≤αk(G)|V(H)|+αk(H)|V(G)|−αk(G)αk(H), and proved the conjecture for k = 1 and k = 2. If true for k = 3 the conjecture strenghtens the result of El-Zahar and Sauer who proved that any direct product of 4-chromatic graphs is 4-chromatic [M. El-Zahar and N. Sauer, The chromatic number of the product of two 4-chromatic graphs is 4, Combinatorica 5 (1985) 121–126]. In this paper we prove that the above bound is true for k = 3 provided that G and H are graphs that have complete tripartite subgraphs of orders α3(G) and α3(H), respectively.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 2; 391-413
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Selkow’s Bound on the Independence Number of Graphs
Autorzy:
Harant, Jochen
Mohr, Samuel
Powiązania:
https://bibliotekanauki.pl/articles/31343349.pdf
Data publikacji:
2019-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
independence number
Opis:
For a graph $G$ with vertex set $ V (G) $ and independence number $ \alpha (G) $, Selkow [A Probabilistic lower bound on the independence number of graphs, Discrete Math. 132 (1994) 363–365] established the famous lower bound \( \sum_{ v \in V (G) } \tfrac{1}{d(v)+1} ( 1+ \max \{ \tfrac{ d(v) }{ d(v)+1 } - \sum_{ u \in N(v) } \tfrac{1}{ d(u)+1 },0 \} ) \) on $ \alpha (G) $, where $ N(v) $ and $ d(v) = | N(v) | $ denote the neighborhood and the degree of a vertex $ v \in V (G) $, respectively. However, Selkow’s original proof of this result is incorrect. We give a new probabilistic proof of Selkow’s bound here.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 3; 655-657
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Independence Number of Traceable 2-Connected Claw-Free Graphs
Autorzy:
Wang, Shipeng
Xiong, Liming
Powiązania:
https://bibliotekanauki.pl/articles/31343185.pdf
Data publikacji:
2019-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
traceability
independence number
matching number
trail
closure
Opis:
A well-known theorem by Chvátal-Erdőos [A note on Hamilton circuits, Discrete Math. 2 (1972) 111–135] states that if the independence number of a graph G is at most its connectivity plus one, then G is traceable. In this article, we show that every 2-connected claw-free graph with independence number α(G) ≤ 6 is traceable or belongs to two exceptional families of well-defined graphs. As a corollary, we also show that every 2-connected claw-free graph with independence number α(G) ≤ 5 is traceable.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 4; 925-937
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Generalized Sierpiński Graphs
Autorzy:
Rodríguez-Velázquez, Juan Alberto
Rodríguez-Bazan, Erick David
Estrada-Moreno, Alejandro
Powiązania:
https://bibliotekanauki.pl/articles/31341732.pdf
Data publikacji:
2017-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Sierpiński graphs
vertex cover number
independence number
chromatic number
domination number
Opis:
In this paper we obtain closed formulae for several parameters of generalized Sierpiński graphs S(G, t) in terms of parameters of the base graph G. In particular, we focus on the chromatic, vertex cover, clique and domination numbers.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 3; 547-560
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Looseness and Independence Number of Triangulations on Closed Surfaces
Autorzy:
Nakamoto, Atsuhiro
Negami, Seiya
Ohba, Kyoji
Suzuki, Yusuke
Powiązania:
https://bibliotekanauki.pl/articles/31340887.pdf
Data publikacji:
2016-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
triangulations
closed surfaces
looseness
k-loosely tight
independence number
Opis:
The looseness of a triangulation $G$ on a closed surface $ F^2$, denoted by $ \xi (G) $, is defined as the minimum number $k$ such that for any surjection $ c : V (G) \rightarrow {1, 2, . . ., k + 3} $, there is a face $uvw$ of $G$ with $c(u)$, $c(v)$ and $c(w)$ all distinct. We shall bound $ \xi (G) $ for triangulations $G$ on closed surfaces by the independence number of $G$ denoted by $ \alpha(G) $. In particular, for a triangulation $G$ on the sphere, we have $ \xi (G) \le \frac{11 \alpha (G) - 10}{6} $ and this bound is sharp. For a triangulation $G$ on a non-spherical surface $F^2$, we have $ \xi (G) \le 2 \alpha (G) + \mathcal{l}(F^2) − 2 $, where $ \mathcal{l}(F^2) = \floor{ (2 − \chi (F^2))//2 } $ with Euler characteristic $ \chi (F^2) $.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 3; 545-554
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Quest for A Characterization of Hom-Properties of Finite Character
Autorzy:
Broere, Izak
Matsoha, Moroli D.V.
Heidema, Johannes
Powiązania:
https://bibliotekanauki.pl/articles/31340894.pdf
Data publikacji:
2016-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
(countable) graph
homomorphism (of graphs)
property of graphs
hom-property
(finitely-)induced-hereditary property
finitely determined property
(weakly) finite character
axiomatizable property
compactness theorems
core
connectedness
chromatic number
clique number
independence number
dominating set
Opis:
A graph property is a set of (countable) graphs. A homomorphism from a graph \( G \) to a graph \( H \) is an edge-preserving map from the vertex set of \( G \) into the vertex set of \( H \); if such a map exists, we write \( G \rightarrow H \). Given any graph \( H \), the hom-property \( \rightarrow H \) is the set of \( H \)-colourable graphs, i.e., the set of all graphs \( G \) satisfying \( G \rightarrow H \). A graph property \( mathcal{P} \) is of finite character if, whenever we have that \( F \in \mathcal{P} \) for every finite induced subgraph \( F \) of a graph \( G \), then we have that \( G \in \mathcal{P} \) too. We explore some of the relationships of the property attribute of being of finite character to other property attributes such as being finitely-induced-hereditary, being finitely determined, and being axiomatizable. We study the hom-properties of finite character, and prove some necessary and some sufficient conditions on \( H \) for \( \rightarrow H \) to be of finite character. A notable (but known) sufficient condition is that \( H \) is a finite graph, and our new model-theoretic proof of this compactness result extends from hom-properties to all axiomatizable properties. In our quest to find an intrinsic characterization of those \( H \) for which \( \rightarrow H \) is of finite character, we find an example of an infinite connected graph with no finite core and chromatic number 3 but with hom-property not of finite character.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 2; 479-500
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Extending the MAX Algorithm for Maximum Independent Set
Autorzy:
Lê, Ngoc C.
Brause, Christoph
Schiermeyer, Ingo
Powiązania:
https://bibliotekanauki.pl/articles/31339469.pdf
Data publikacji:
2015-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
maximum independent set
stable set
stability number
independence number
reduction
graph transformation
MAX Algorithm
MIN Algorithm
Vertex Order Algorithm
Opis:
The maximum independent set problem is an NP-hard problem. In this paper, we consider Algorithm MAX, which is a polynomial time algorithm for finding a maximal independent set in a graph G. We present a set of forbidden induced subgraphs such that Algorithm MAX always results in finding a maximum independent set of G. We also describe two modifications of Algorithm MAX and sets of forbidden induced subgraphs for the new algorithms.
Źródło:
Discussiones Mathematicae Graph Theory; 2015, 35, 2; 365-386
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the independence number of edge chromatic critical graphs
Autorzy:
Pang, Shiyou
Miao, Lianying
Song, Wenyao
Miao, Zhengke
Powiązania:
https://bibliotekanauki.pl/articles/30148675.pdf
Data publikacji:
2014-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
edge coloring
edge-chromatic critical graphs
independence number
Opis:
In 1968, Vizing conjectured that for any edge chromatic critical graph $G = (V,E)$ with maximum degree $△$ and independence number $α(G)$, $α(G) ≤ \frac{|V|}{2}$. It is known that $α(G) < \frac{3∆−2}{5∆−2}|V|$. In this paper we improve this bound when $△≥4$. Our precise result depends on the number $n_2$ of 2-vertices in $G$, but in particular we prove that $α(G) ≤\frac{3∆−3}{5∆−3}|V|$ when $△≥5$ and $n_2≤2(△− 1)$.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 3; 577-584
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 29

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