An __acyclic edge‐coloring__ of a graph is a proper edge‐coloring such that the subgraph induced by the edges of any two colors is acyclic. The __acyclic chromatic index__ of a graph __G__ is the smallest number of colors in an acyclic edge‐coloring of __G__. We prove that the acyclic chromatic inde
Change graphs of edge-colorings of planar cubic graphs
✍ Scribed by Anton Kotzig
- Publisher
- Elsevier Science
- Year
- 1977
- Tongue
- English
- Weight
- 291 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0095-8956
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In this paper we present a short algebraic proof for a generalization of a formula of R. Penrose, Some applications of negative dimensional tensors, in: Combinatorial Mathematics and its Applications Welsh (ed.), Academic Press, 1971, pp. 221-244 on the number of 3-edge colorings of a plane cubic gr
## Abstract A proper coloring of the edges 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 __a′__(__G__), is the least number of colors in an acyclic edge coloring of __G__. For certain graphs __G__, __a′__(_
Let x'(G), called the strong coloring number of G, denote the minimum number of colors for which there is a proper edge coloring of a graph G in which no two of its vertices is incident to edges colored with the same set of colors. It is shown that Z'~(G) ~< Fcn], ½ < c ~ 1, whenever A(G) is appropr
## Abstract A (1,2)‐eulerian weight __w__ of a grph is hamiltonian if every faithful cover of __w__ is a set of two Hamilton circuits. Let __G__ be a 3‐connected cubic graph containing no subdivition of the Petersen graph. We prove that if __G__ admits a hamiltonian weight then __G__ is uniquely 3‐