## 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_
The complexity of chromatic strength and chromatic edge strength
✍ Scribed by Dániel Marx
- Publisher
- Springer
- Year
- 2006
- Tongue
- English
- Weight
- 341 KB
- Volume
- 14
- Category
- Article
- ISSN
- 1016-3328
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## Abstract Circular chromatic number, χ~__c__~ is a natural generalization of chromatic number. It is known that it is **NP**‐hard to determine whether or not an arbitrary graph __G__ satisfies χ(__G__)=χ~__c__~(__G__). In this paper we prove that this problem is **NP**‐hard even if the chromatic
## Abstract A proper edge coloring of a graph __G__ is called acyclic if there is no 2‐colored cycle in __G__. The acyclic edge chromatic number of __G__, denoted by χ(__G__), is the least number of colors in an acyclic edge coloring of __G__. In this paper, we determine completely the acyclic edge
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