## Abstract A proper edge coloring of a graph __G__ is called acyclic if there is no 2βcolored cycle in __G__. The acyclic edge chromatic number of __G__, denoted by Ο(__G__), is the least number of colors in an acyclic edge coloring of __G__. In this paper, we determine completely the acyclic edge
Edge Separators of Planar and Outerplanar Graphs With Applications
β Scribed by K. Diks; H.N. Djidjev; O. Sykora; I. Vrto
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 816 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0196-6774
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π SIMILAR VOLUMES
## Abstract The object of this paper is to show tht every planar graph of minimum valency 5 is reconstructible from its family of edgeβdeleted subgraphs.
It is proved that any edge of a Pconnected non-planar graph G of order a t least 6 lies in a subdivision of K3,3 in G. For any 3-connected non-planar graph G of order a t least 6 we show that G contains at most four edges which belong to no subdivisions of K3,3 in G.
## Abstract The object of this paper is to show that 4βconnected planar graphs are uniquely determined from their collection of edgeβdeleted subgraphs.
An __acyclic__ edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The __acyclic chromatic index__ of a graph is the minimum number __k__ such that there is an acyclic edge coloring using __k__ colors and is denoted by __a__β²(__G__). It was conjectured by Al
## Abstract We prove that every simple cubic planar graph admits a planar embedding such that each edge is embedded as a straight line segment of integer length. Β© 2008 Wiley Periodicals, Inc. J Graph Theory 58:270β274, 2008