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Tytuł:
Perfect connected-dominant graphs
Autorzy:
Zverovich, Igor
Powiązania:
https://bibliotekanauki.pl/articles/743393.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Connected domination
perfect connected-dominant graph
Opis:
If D is a dominating set and the induced subgraph G(D) is connected, then D is a connected dominating set. The minimum size of a connected dominating set in G is called connected domination number $γ_c(G)$ of G. A graph G is called a perfect connected-dominant graph if $γ(H) = γ_c(H)$ for each connected induced subgraph H of G.We prove that a graph is a perfect connected-dominant graph if and only if it contains no induced path P₅ and induced cycle C₅.
Źródło:
Discussiones Mathematicae Graph Theory; 2003, 23, 1; 159-162
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The connected forcing connected vertex detour number of a graph
Autorzy:
Santhakumaran, A.
Titus, P.
Powiązania:
https://bibliotekanauki.pl/articles/743939.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
vertex detour number
connected vertex detour number
upper connected vertex detour number
forcing connected vertex detour number
connected forcing connected vertex detour number
Opis:
For any vertex x in a connected graph G of order p ≥ 2, a set S of vertices of V is an x-detour set of G if each vertex v in G lies on an x-y detour for some element y in S. A connected x-detour set of G is an x-detour set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected x-detour set of G is the connected x-detour number of G and is denoted by cdₓ(G). For a minimum connected x-detour set Sₓ of G, a subset T ⊆ Sₓ is called a connected x-forcing subset for Sₓ if the induced subgraph G[T] is connected and Sₓ is the unique minimum connected x-detour set containing T. A connected x-forcing subset for Sₓ of minimum cardinality is a minimum connected x-forcing subset of Sₓ. The connected forcing connected x-detour number of Sₓ, denoted by $cf_{cdx}(Sₓ)$, is the cardinality of a minimum connected x-forcing subset for Sₓ. The connected forcing connected x-detour number of G is $cf_{cdx}(G) = mincf_{cdx}(Sₓ)$, where the minimum is taken over all minimum connected x-detour sets Sₓ in G. Certain general properties satisfied by connected x-forcing sets are studied. The connected forcing connected vertex detour numbers of some standard graphs are determined. It is shown that for positive integers a, b, c and d with 2 ≤ a < b ≤ c ≤ d, there exists a connected graph G such that the forcing connected x-detour number is a, connected forcing connected x-detour number is b, connected x-detour number is c and upper connected x-detour number is d, where x is a vertex of G.
Źródło:
Discussiones Mathematicae Graph Theory; 2011, 31, 3; 461-473
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A New Proof that 4-Connected Planar Graphs are Hamiltonian-Connected
Autorzy:
Lu, Xiaoyun
West, Douglas B.
Powiązania:
https://bibliotekanauki.pl/articles/31340879.pdf
Data publikacji:
2016-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
4-connected planar graph
Hamiltonian-connected
Tutte-path
Opis:
We prove a theorem guaranteeing special paths of faces in 2-connected plane graphs. As a corollary, we obtain a new proof of Thomassen’s theorem that every 4-connected planar graph is Hamiltonian-connected.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 3; 555-564
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Weakly connected domination subdivision numbers
Autorzy:
Raczek, Joanna
Powiązania:
https://bibliotekanauki.pl/articles/743529.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
weakly connected domination number
weakly connected domination subdivision number
Opis:
A set D of vertices in a graph G = (V,E) is a weakly connected dominating set of G if D is dominating in G and the subgraph weakly induced by D is connected. The weakly connected domination number of G is the minimum cardinality of a weakly connected dominating set of G. The weakly connected domination subdivision number of a connected graph G is the minimum number of edges that must be subdivided (where each egde can be subdivided at most once) in order to increase the weakly connected domination number. We study the weakly connected domination subdivision numbers of some families of graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2008, 28, 1; 109-119
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Connected Domination Critical Graphs with Cut Vertices
Autorzy:
Kaemawichanurat, Pawaton
Ananchuen, Nawarat
Powiązania:
https://bibliotekanauki.pl/articles/31348137.pdf
Data publikacji:
2020-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
connected domination
critical
Opis:
A graph G is said to be k-γc-critical if the connected domination number of G, γc(G), is k and γc(G + uv) < k for any pair of non-adjacent vertices u and v of G. Let G be a k-γc-critical graph and ζ (G) the number of cut vertices of G. It was proved, in [1, 6], that, for 3 ≤ k ≤ 4, every k-γc-critical graph satisfies ζ (G) ≤ k − 2. In this paper, we generalize that every k-γc-critical graph satisfies ζ (G) ≤ k − 2 for all k ≥ 5. We also characterize all k-γc-critical graphs when ζ(G) is achieving the upper bound.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 4; 1035-1055
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Domination numbers in graphs with removed edge or set of edges
Autorzy:
Lemańska, Magdalena
Powiązania:
https://bibliotekanauki.pl/articles/744295.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
connected domination number
weakly connected domination number
edge removal
Opis:
It is known that the removal of an edge from a graph G cannot decrease a domination number γ(G) and can increase it by at most one. Thus we can write that γ(G) ≤ γ(G-e) ≤ γ(G)+1 when an arbitrary edge e is removed. Here we present similar inequalities for the weakly connected domination number $γ_w$ and the connected domination number $γ_c$, i.e., we show that $γ_w(G) ≤ γ_w(G-e) ≤ γ_w(G)+1$ and $γ_c(G) ≤ γ_c(G-e) ≤ γ_c(G) + 2$ if G and G-e are connected. Additionally we show that $γ_w(G) ≤ γ_w(G-Eₚ) ≤ γ_w(G) + p - 1$ and $γ_c(G) ≤ γ_c(G -Eₚ) ≤ γ_c(G) + 2p - 2$ if G and G - Eₚ are connected and Eₚ = E(Hₚ) where Hₚ of order p is a connected subgraph of G.
Źródło:
Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 51-56
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Edge-Connectivity and Edges of Even Factors of Graphs
Autorzy:
Haghparast, Nastaran
Kiani, Dariush
Powiązania:
https://bibliotekanauki.pl/articles/31343450.pdf
Data publikacji:
2019-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
3-edge-connected graph
2-edge-connected graph
even factor
component
Opis:
An even factor of a graph is a spanning subgraph in which each vertex has a positive even degree. Jackson and Yoshimoto showed that if G is a 3-edge-connected graph with |G| ≥ 5 and v is a vertex with degree 3, then G has an even factor F containing two given edges incident with v in which each component has order at least 5. We prove that this theorem is satisfied for each pair of adjacent edges. Also, we show that each 3-edge-connected graph has an even factor F containing two given edges e and f such that every component containing neither e nor f has order at least 5. But we construct infinitely many 3-edge-connected graphs that do not have an even factor F containing two arbitrary prescribed edges in which each component has order at least 5.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 2; 357-364
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Improved Sufficient Conditions for Hamiltonian Properties
Autorzy:
Bode, Jens-P.
Fricke, Anika
Kemnitz, Arnfried
Powiązania:
https://bibliotekanauki.pl/articles/31339476.pdf
Data publikacji:
2015-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Hamiltonian
traceable
Hamiltonian-connected
Opis:
In 1980 Bondy [2] proved that a (k+s)-connected graph of order n ≥ 3 is traceable (s = −1) or Hamiltonian (s = 0) or Hamiltonian-connected (s = 1) if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1)(n+s−1)+1)/2. It is shown in [1] that one can allow exceptional (k+1)-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity condition.
Źródło:
Discussiones Mathematicae Graph Theory; 2015, 35, 2; 329-334
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique Number
Autorzy:
Volkmann, Lutz
Powiązania:
https://bibliotekanauki.pl/articles/31343389.pdf
Data publikacji:
2019-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
edge-connectivity
clique number
maximally edge-connected graphs
super-edge-connected graphs
Opis:
Let G be a connected graph with minimum degree δ and edge-connectivity λ. A graph is maximally edge-connected if λ = δ, and it is super-edgeconnected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. The clique number ω(G) of a graph G is the maximum cardinality of a complete subgraph of G. In this paper, we show that a connected graph G with clique number ω(G) ≤ r is maximally edge-connected or super-edge-connected if the number of edges is large enough. These are generalizations of corresponding results for triangle-free graphs by Volkmann and Hong in 2017.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 2; 567-573
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Note on Cycles in Locally Hamiltonian and Locally Hamilton-Connected Graphs
Autorzy:
Tang, Long
Vumar, Elkin
Powiązania:
https://bibliotekanauki.pl/articles/32032199.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
locally connected
locally Hamiltonian
locally Hamilton-connected
fully cycle extendability
weakly pancyclicity
Opis:
Let \(\mathcal{P}\) be a property of a graph. A graph G is said to be locally \(\mathcal{P}\), if the subgraph induced by the open neighbourhood of every vertex in G has property \(\mathcal{P}\). Ryjáček conjectures that every connected, locally connected graph is weakly pancyclic. Motivated by the above conjecture, van Aardt et al. [S.A.van Aardt, M. Frick, O.R. Oellermann and J.P.de Wet, Global cycle properties in locally connected, locally traceable and locally Hamiltonian graphs, Discrete Appl. Math. 205 (2016) 171–179] investigated the global cycle structures in connected, locally traceable/Hamiltonian graphs. Among other results, they proved that a connected, locally Hamiltonian graph G with maximum degree at least |V (G)| − 5 is weakly pancyclic. In this note, we improve this result by showing that such a graph with maximum degree at least |V (G)|−6 is weakly pancyclic. Furthermore, we show that a connected, locally Hamilton-connected graph with maximum degree at most 7 is fully cycle extendable.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 77-84
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Proper Diameter of a Graph
Autorzy:
Coll, Vincent
Hook, Jonelle
Magnant, Colton
McCready, Karen
Ryan, Kathleen
Powiązania:
https://bibliotekanauki.pl/articles/32062335.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
diameter
properly connected
proper diameter
Opis:
A proper edge-coloring of a graph is a coloring in which adjacent edges receive distinct colors. A path is properly colored if consecutive edges have distinct colors, and an edge-colored graph is properly connected if there exists a properly colored path between every pair of vertices. In such a graph, we introduce the notion of the graph’s proper diameter—which is a function of both the graph and the coloring—and define it to be the maximum length of a shortest properly colored path between any two vertices in the graph. We consider various families of graphs to find bounds on the gap between the diameter and possible proper diameters, paying singular attention to 2-colorings.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 107-125
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Balanced Decomposition Number of $ TK_4 $ and Series-Parallel Graphs
Autorzy:
Fujita, Shinya
Liu, Henry
Powiązania:
https://bibliotekanauki.pl/articles/30146584.pdf
Data publikacji:
2013-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph decomposition
vertex colouring
k-connected
Opis:
A balanced colouring of a graph $G$ is a colouring of some of the vertices of $G$ with two colours, say red and blue, such that there is the same number of vertices in each colour. The balanced decomposition number $f(G)$ of $G$ is the minimum integer $s$ with the following property: For any balanced colouring of $G$, there is a partition $ V (G) = V_1 \dot\cup ... \dot\cup V_r $ such that, for every $i$, $V_i$ induces a connected subgraph of order at most $s$, and contains the same number of red and blue vertices. The function $f(G)$ was introduced by Fujita and Nakamigawa in 2008. They conjectured that $f(G) \le \floor(\frac{n}{2}) + 1$ if $G$ is a 2-connected graph on $n$ vertices. In this paper, we shall prove two partial results, in the cases when $G$ is a subdivided $K_4$, and a 2-connected series-parallel graph.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 2; 347-359
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Connected partition dimensions of graphs
Autorzy:
Saenpholphat, Varaporn
Zhang, Ping
Powiązania:
https://bibliotekanauki.pl/articles/743364.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
distance
resolving partition
connected resolving partition
Opis:
For a vertex v of a connected graph G and a subset S of V(G), the distance between v and S is d(v,S) = min{d(v,x)|x ∈ S}. For an ordered k-partition Π = {S₁,S₂,...,Sₖ} of V(G), the representation of v with respect to Π is the k-vector r(v|Π) = (d(v,S₁), d(v,S₂),..., d(v,Sₖ)). The k-partition Π is a resolving partition if the k-vectors r(v|Π), v ∈ V(G), are distinct. The minimum k for which there is a resolving k-partition of V(G) is the partition dimension pd(G) of G. A resolving partition Π = {S₁,S₂,...,Sₖ} of V(G) is connected if each subgraph $⟨S_i⟩$ induced by $S_i$ (1 ≤ i ≤ k) is connected in G. The minimum k for which there is a connected resolving k-partition of V(G) is the connected partition dimension cpd(G) of G. Thus 2 ≤ pd (G) ≤ cpd(G) ≤ n for every connected graph G of order n ≥ 2. The connected partition dimensions of several classes of well-known graphs are determined. It is shown that for every pair a, b of integers with 3 ≤ a ≤ b ≤ 2a-1, there is a connected graph G having pd(G) = a and cpd(G) = b. Connected graphs of order n ≥ 3 having connected partition dimension 2, n, or n-1 are characterized.
Źródło:
Discussiones Mathematicae Graph Theory; 2002, 22, 2; 305-323
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Long induced paths in 3-connected planar graphs
Autorzy:
Arocha, Jorge
Valencia, Pilar
Powiązania:
https://bibliotekanauki.pl/articles/743721.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
induced paths
3-connected planar graphs
Opis:
It is shown that every 3-connected planar graph with a large number of vertices has a long induced path.
Źródło:
Discussiones Mathematicae Graph Theory; 2000, 20, 1; 105-107
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on minimally 3-connected graphs
Autorzy:
Neumann-Lara, Víctor
Rivera-Campo, Eduardo
Urrutia, Jorge
Powiązania:
https://bibliotekanauki.pl/articles/744439.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
minimally 3-connected
walk double cover
Opis:
If G is a minimally 3-connected graph and C is a double cover of the set of edges of G by irreducible walks, then |E(G)| ≥ 2| C| - 2.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 1; 115-123
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 43

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