Results 81 to 90 of about 113,121 (99)
Vizing’s conjecture: A two-thirds bound for claw-free graphs
Discrete Applied Mathematics, 2017 We show that for any claw-free graph $G$ and any graph $H$, $γ(G\square H)\geq \frac{2}{3}γ(G)γ(H)$, where $γ(G)$ is the domination number of $G$.
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Vizing's Conjecture for Graphs with Domination Number 3 - a New Proof
The Electronic Journal of Combinatorics, 2015 Vizing's conjecture from 1968 asserts that the domination number of the Cartesian product of two graphs is at least as large as the product of their domination numbers. In this note we use a new, transparent approach to prove Vizing's conjecture for graphs with domination number 3; that is, we prove that for any graph $G$ with $\gamma(G)=3$ and an ...
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On two conjectures to generalize Vizing's theorem
Le Matematiche, 1990 Summary: Vizing's theorem states that for a simple graph \(G\), the chromatic index \(q(G)\) is equal to the maximum degree \(\Delta(G)\) or to \(\Delta(G)+1\). To extend this theorem to some classes of hypergraphs, we suggested two conjectures, non-comparable, but, in some sense, dual, which are discussed in the present paper.
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A brief, simple proof of Vizing's conjecture
, 2011 This paper has been withdrawn by the author due to a problem with the "label exchange"
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On Convex Subcomplexes of Spherical Buildings and Tits’ Center Conjecture [PDF]
, 2009 In this thesis we study convex subcomplexes of spherical buildings. In particular, we are interested in a question of J. Tits which goes back to the 50’s, the so-called Center Conjecture.
Ramos Cuevas, Carlos
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Supermodular Extension of Vizing's Edge-Coloring Theorem [PDF]
K\H{o}nig's edge-coloring theorem for bipartite graphs and Vizing's edge-coloring theorem for general graphs are celebrated results in graph theory and combinatorial optimization.
Mizutani, Ryuhei
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Vizing's conjecture: a survey and recent results
, 2012 Vizingova domneva iz leta 1968 trdi, da je dominacijsko število kartezičnega produkta dveh grafov vsaj tako veliko, kot je produkt dominacijskih števil faktorjev. V članku naredimo pregled različnih pristopov k tej osrednji domnevi iz teorije grafovske dominacije. Ob tem dokažemo tudi nekaj novih rezultatov.
Brešar, Boštjan +6 more
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Domination Density and an Imbalance Regime for Vizings Conjecture
8 pages, 2 ...
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A partition approach to Vizing's conjecture
Journal of Graph Theory, 1996One conjecture of V. G. Vizing says that \(\gamma(G\times H)\geq \gamma(G) \gamma(H)\), where \(\gamma\) is the domination number of a graph. The authors prove the inequalities \(P_2(G)\leq x(G)\leq \gamma(G)\) and \(\gamma(G\times H)\geq x(G) \gamma(H)\). The symbol \(P_2(G)\) denotes the 2-packing number of \(G\), i.e.
Guantao Chen +2 more
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