Results 21 to 30 of about 14,237 (338)
List coloring of Cartesian products of graphs
Discrete Mathematics, 2006 A well-established generalization of graph coloring is the concept of list coloring. In this setting, each vertex v of a graph G is assigned a list L(v) of k colors and the goal is to find a proper coloring c of G with c(v)∈L(v).
Mieczysław Borowiecki +2 more
exaly +2 more sources
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
doaj +7 more sources
A Note on Partial List Colorings [PDF]
Australas. J Comb., 2008 Let $G$ be a simple graph with $n$ vertices and list chromatic number $χ_\ell(G)=χ_\ell$. Suppose that $0\leq t\leq χ_\ell$ and each vertex of $G$ is assigned a list of $t$ colors. Albertson, Grossman and Haas [1] conjectured that at least $\frac{tn}{χ_\ell}$ vertices of $G$ can be colored from these lists.
Moharram N. Iradmusa
openaire +4 more sources
On-line list coloring of matroids
Discrete Applied Mathematics, 2017 A coloring of a matroid is proper if elements of the same color form an independent set. A theorem of Seymour asserts that a k-colorable matroid is also colorable from any lists of size k. We prove an on-line version of this theorem.
Lubawski, Wojciech, Lason, Michael
core +4 more sources
The Electronic Journal of Combinatorics, 2017 In this paper, we introduce a new variation of list-colorings. For a graph $G$ and for a given nonnegative integer $t$, a $t$-common list assignment of $G$ is a mapping $L$ which assigns each vertex $v$ a set $L(v)$ of colors such that given set of $t$ colors belong to $L(v)$ for every $v\in V(G)$.
Hojin Choi, Young Soo Kwon
openaire +3 more sources
Discrete Mathematics, 2003 We study the function f(G) defined for a graph G as the smallest integer k such that the join of G with a stable set of size k is not |V(G)|-choosable. This function was introduced recently in order to describe extremal graphs for a list-coloring version
Maffray, Frédéric +5 more
core +3 more sources
Coloring, List Coloring, and Painting Squares of Graphs (and other related problems) [PDF]
, 2023 We survey work on coloring, list coloring, and painting squares of graphs; in particular, we consider strong edge-coloring. We focus primarily on planar graphs and other sparse classes of graphs.Comment: 32 pages, 13 figures and tables, plus 195-entry ...
Cranston, Daniel W.
core +2 more sources
Three-coloring and list three-coloring of graphs without induced paths on seven vertices [PDF]
, 2017 In this paper we present a polynomial time algorithm that determines if an input graph containing no induced seven-vertex path is 3-colorable. This affirmatively answers a question posed by Randerath, Schiermeyer and Tewes in 2002.
Maceli, Peter +11 more
core +3 more sources
Hajós' theorem for list coloring
Discrete Mathematics, 2004 We study an analogue of Hajós' theorem for list coloring which states that each non-k-choosable graph can be obtained from any non-k-choosable complete bipartite graph by a certain set of graph operations.
Král', Daniel
core +2 more sources
Graph choosability and double list colorability [PDF]
Opuscula Mathematica, 2010 In this paper, we give a sufficient condition for graph choosability, based on Combinatorial Nullstellensatz and a specific property, called "double list colorability", which means that there is a list assignment for which there are exactly two ...
Hamid-Reza Fanaï
doaj +1 more source