Results 71 to 80 of about 215 (116)
Fractional coloring with local demands
, 2018 We investigate fractional colorings of graphs in which the amount of color given to a vertex depends on local parameters, such as its degree or the clique number of its neighborhood; in a \textit{fractional $f$-coloring}, vertices are given color from ...
Kelly, Tom, Postle, Luke
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On a Vizing-like conjecture for direct product graphs
Discrete Mathematics, 1996 A subset \(D\) of the vertex set \(V(G)\) of a graph \(G\) is called dominating, if for each \(x \in V(G) - D\) there exists \(y \in D\) adjacent to \(x\). The minimum number of vertices of a dominating set of \(G\) is called the domination number \(\gamma (G)\) of \(G\).
Klavẑar, Sandi, Zmazek, Blaẑ
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Cliques, Degrees, and Coloring: Expanding the ω, Δ, χ paradigm [PDF]
, 2019 Many of the most celebrated and influential results in graph coloring, such as Brooks' Theorem and Vizing's Theorem, relate a graph's chromatic number to its clique number or maximum degree.
Kelly, Thomas
core
Domination in graphs: Vizing's conjecture
, 2022 Vizing's conjecture remains one of the biggest open problems in domination in graph theory today. The conjecture states that the domination number of the Cartesian product of two graphs is at least as large as the product of the domination numbers of the two factor graphs.
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Extremal problems on counting combinatorial structures [PDF]
, 2017 The fast developing field of extremal combinatorics provides a diverse spectrum of powerful tools with many applications to economics, computer science, and optimization theory. In this thesis, we focus on counting and coloring problems in this field.
Petrickova, Sarka
core
Vizing's Conjecture for Almost All Pairs of Graphs
, 2015 5 ...
Contractor, Aziz, Krop, Elliot
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Distance measures in graphs and subgraphs. [PDF]
, 1996 Thesis (M.Sc.)-University of Natal, 1996.In this thesis we investigate how the modification of a graph affects various distance measures. The questions considered arise in the study of how the efficiency of communications networks is affected by the ...
Swart, Christine Scott.
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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 $H$, $ (G\square H)\geq \frac{2}{3} (G) (H)$, where $ (G)$ is the domination number of $G$.
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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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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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