Equitable and equitable list colorings of graphs
نویسندگان
چکیده
منابع مشابه
Equitable List Coloring of Graphs
A graph G is equitably k-choosable if, for any k-uniform list assignment L, G admits a proper coloring π such that π(v) ∈ L(v) for all v ∈ V (G) and each color appears on at most |G|/k vertices. It was conjectured in [8] that every graph G with maximum degree ∆ is equitably k-choosable whenever k ≥ ∆ + 1. We prove the conjecture for the following cases: (i) ∆ ≤ 3; (ii) k ≥ (∆ − 1). Moreover, eq...
متن کاملEquitable Online-Colorings of Random Graphs
A proper graph coloring is called equitable if the sizes of every two color classes differ by at most one. We consider the following generalized notion of graph colorings: a vertex coloring of graph G is valid w.r.t. some fixed nonempty graph F if no color class induces a copy of F in G, i.e., there is no monochromatic copy of F in G. We propose and analyze an algorithm for computing valid equi...
متن کاملEquitable Colorings of Bounded Treewidth Graphs
A proper coloring of a graph G is equitable if the sizes of any two color classes are differ by at most one. The related notion is `-bounded coloring where each of the color classes is of cardinality ≤ `. We consider the problems to determine for a given graph G (and a given integer `) whether G has an equitable (`-bounded) coloring. We prove that both problems can be solved in polynomial time ...
متن کاملEquitable colorings of corona multiproducts of graphs
A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted χ=(G). It is known that this problem is NP-hard in general case and remains so for corona graphs. In [12] Lin i Chan...
متن کاملNote on equitable colorings of graphs
An equitable coloring of a graph G is a proper coloring of the vertices of G such that color classes differ in size by at most one. In this note, we verify the equitable coloring conjecture [W. Meyer, Amer. Math. Monthly 80 (1973), 920–922] for some classes of graphs which are defined by forbidden induced subgraphs using known results.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2010
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2010.06.027