Results 11 to 20 of about 115,985 (312)
Random Structures & Algorithms, 2023 AbstractList coloring is an influential and classic topic in graph theory. We initiate the study of a natural strengthening of this problem, where instead of one list‐coloring, we seek many in parallel. Our explorations have uncovered a potentially rich seam of interesting problems spanning chromatic graph theory. Given a ‐list‐assignment of a graph ,
Stijn Cambie +3 more
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Kempe Equivalent List Colorings Revisited [PDF]
Journal of Graph Theory, 2022 AbstractA Kempe chain on colors and is a component of the subgraph induced by colors and . A Kempe change is the operation of interchanging the colors of some Kempe chains. For a list‐assignment and an ‐coloring , a Kempe change is ‐valid for if performing the Kempe change yields another ‐coloring. Two ‐colorings are ‐equivalent if we can form one
Dibyayan Chakraborty +2 more
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List Coloring Hypergraphs [PDF]
The Electronic Journal of Combinatorics, 2010 Let $H$ be a hypergraph and let $L_v : v \in V(H)$ be sets; we refer to these sets as lists and their elements as colors. A list coloring of $H$ is an assignment of a color from $L_v$ to each $v \in V(H)$ in such a way that every edge of $H$ contains a pair of vertices of different colors.
Penny Haxell, Jacques Verstraëte
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Generalized Sum List Colorings of Graphs
Discussiones Mathematicae Graph Theory, 2019 A (graph) property 𝒫 is a class of simple finite graphs closed under isomorphisms. In this paper we consider generalizations of sum list colorings of graphs with respect to properties 𝒫.
Kemnitz Arnfried +2 more
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Some Conclusion on Unique k-List Colorable Complete Multipartite Graphs
Journal of Applied Mathematics, 2013 If a graph G admits a k-list assignment L such that G has a unique L-coloring, then G is called uniquely k-list colorable graph, or UkLC graph for short.
Yanning Wang, Yanyan Wang, Xuguang Zhang
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Journal of Graph Theory, 2015 AbstractThe dichromatic number of a digraph D is the least number k such that the vertex set of D can be partitioned into k parts each of which induces an acyclic subdigraph. Introduced by Neumann‐Lara in 1982, this digraph invariant shares many properties with the usual chromatic number of graphs and can be seen as the natural analog of the graph ...
Julien Bensmail +2 more
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List Coloring Triangle-Free Hypergraphs [PDF]
Random Structures & Algorithms, 2013 A triangle in a hypergraph is a collection of distinct vertices u,v,w and distinct edges e,f,g with u,v \in e, v,w \in f, w,u \in g, and \{u,v,w\} \cap e \cap f \cap g=\emptyset. The i-degree of a vertex in a hypergraph is the number of edges of size i containing it.
Jeff Cooper, Dhruv Mubayi
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Parameterized Pre-Coloring Extension and List Coloring Problems [PDF]
SIAM Journal on Discrete Mathematics, 2021 Golovach, Paulusma and Song (Inf. Comput. 2014) asked to determine the parameterized complexity of the following problems parameterized by $k$: (1) Given a graph $G$, a clique modulator $D$ (a clique modulator is a set of vertices, whose removal results in a clique) of size $k$ for $G$, and a list $L(v)$ of colors for every $v\in V(G)$, decide whether $
Gregory Gutin +3 more
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Total Equitable List Coloring [PDF]
Graphs and Combinatorics, 2018 An equitable coloring is a proper coloring of a graph such that the sizes of the color classes differ by at most one. A graph $G$ is equitably $k$-colorable if there exists an equitable coloring of $G$ which uses $k$ colors, each one appearing on either $\lfloor |V(G)|/k \rfloor$ or $\lceil |V(G)|/k \rceil$ vertices of $G$. In 1994, Fu conjectured that
Kaul, Hemanshu +2 more
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Kempe Equivalent List Colorings
Combinatorica, 2023 29 pages, 12 figures; second version extends the main result to cliques, which were previously excluded; third version incorporates reviewer feedback; to appear in ...
Cranston, Daniel W., Mahmoud, Reem
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