منابع مشابه
Near-optimal list colorings
We show that a simple variant of a naive colouring procedure can be used to list colour the edges of a k-uniform linear hypergraph of maximum degree provided every vertex has a list of at least +c(log) 4 1? 1 k available colours (where c is a constant which depends on k). We can extend this to colour hypergraphs of maximum codegree o(() with + o(() colours. This improves earlier results of Kahn...
متن کاملPartial list colorings
Suppose G is an s-choosable graph with n vertices, and every vertex of G is assigned a list of t colors. We conjecture that at least t s · n of the vertices of G can be colored from these lists. We provide lower bounds and consider related questions. For instance we show that if G is χ-colorable (rather than being s-choosable), then more than ( 1 − ( χ−1 χ )t) · n of the vertices of G can be co...
متن کاملList-Distinguishing Colorings of Graphs
A coloring of the vertices of a graph G is said to be distinguishing provided that no nontrivial automorphism of G preserves all of the vertex colors. The distinguishing number of G, denoted D(G), is the minimum number of colors in a distinguishing coloring of G. The distinguishing number, first introduced by Albertson and Collins in 1996, has been widely studied and a number of interesting res...
متن کاملRestricted List Colorings of Graphs
A graph is called to be uniquely list colorable, if it admits a list assignment which induces a unique list coloring. We study uniquely list colorable graphs with a restriction on the number of colors used. In this way we generalize a theorem which characterizes uniquely 2–list colorable graphs. We introduce the uniquely list chromatic number of a graph and make a conjecture about it which is a...
متن کاملList colorings with measurable sets
The measurable list chromatic number of a graph G is the smallest number ξ such that if each vertex v of G is assigned a set L(v) of measure ξ in a fixed atomless measure space, then there exist sets c(v) ⊆ L(v) such that each c(v) has measure one and c(v) ∩ c(v′) = ∅ for every pair of adjacent vertices v and v′. We provide a simpler proof of a measurable generalization of Hall’s theorem due to...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1997
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(97)00046-2