منابع مشابه
Facial colorings using Hall's Theorem
A vertex coloring of a plane graph is `-facial if every two distinct vertices joined by a facial walk of length at most ` receive distinct colors. It has been conjectured that every plane graph has an `-facial coloring with at most 3` + 1 colors. We improve the currently best known bound and show that every plane graph has an `-facial coloring with at most b7`/2c + 6 colors. Our proof uses the ...
متن کاملCyclic 4-Colorings of Graphs on Surfaces
To attack the Four Color Problem, in 1880, Tait gave a necessary and sufficient condition for plane triangulations to have a proper 4-vertex-coloring: a plane triangulation G has a proper 4-vertex-coloring if and only if the dual of G has a proper 3-edge-coloring. A cyclic coloring of a map G on a surface F 2 is a vertex-coloring of G such that any two vertices x and y receive different colors ...
متن کاملInterval cyclic edge-colorings of graphs
A proper edge-coloring of a graph G with colors 1, , t is called an interval cyclic t coloring if all colors are used, and the edges incident to each vertex ( ) v V G are colored with ( ) G d v consecutive colors by modulo t , where ( ) G d v is the degree of the vertex v in G . In this paper some properties of interval cyclic edge-colorings are investigated. Also, we give some bounds for...
متن کاملCompact cyclic edge-colorings of graphs
The paper is devoted to the model of compact cyclic edge-coloring. This variant of edge-coloring finds its applications in modeling schedules in production systems, in which production proceeds in a cyclic way. We point out optimal colorings for some graph classes and we construct graphs which cannot be colored in a compact cyclic manner. Moreover, we prove some theoretical properties of consid...
متن کاملDiagonal Stability for a Class of Cyclic Systems and Applications
We consider a class of systems with a cyclic structure that arises, among other examples, in dynamic models for certain biochemical reactions. We first show that a criterion for local stability, derived earlier in the literature, is in fact a necessary and sufficient condition for diagonal stability of the corresponding class of matrices. We then revisit a recent generalization of this criterio...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2005
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2004.01.016