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Cyclic Chromatic Number of 3-Connected Plane Graphs

✍ Scribed by Enomoto, Hikoe; Hornák, Mirko; Jendrol', Stanislav

Book ID
118198139
Publisher
Society for Industrial and Applied Mathematics
Year
2001
Tongue
English
Weight
200 KB
Volume
14
Category
Article
ISSN
0895-4801

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📜 SIMILAR VOLUMES

A general upper bound for the cyclic chr
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## Abstract The cyclic chromatic number of a plane graph __G__ is the smallest number χ~__c__~(__G__) of colors that can be assigned to vertices of __G__ in such a way that whenever two distinct vertices are incident with a common face, they receive distinct colors. It was conjectured by Plummer an

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## Abstract Given a simple plane graph __G__, an edge‐face __k__‐coloring of __G__ is a function ϕ : __E__(__G__) ∪ __F__(G) →  {1,…,__k__} such that, for any two adjacent or incident elements __a__, __b__ ∈ __E__(__G__) ∪ __F__(__G__), ϕ(__a__) ≠ ϕ(__b__). Let χ~e~(__G__), χ~ef~(__G__), and Δ(__G_

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✍ W. Weifan 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 35 KB

The entire chromatic number χ ve f (G) of a plane graph G is the least number of colors assigned to the vertices, edges and faces so that every two adjacent or incident pair of them receive different colors. conjectured that χ ve f (G) ≤ + 4 for every plane graph G. In this paper we prove the conj