The strong chromatic index of complete cubic Halin graphs
โ Scribed by W.C. Shiu; W.K. Tam
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 809 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0893-9659
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โฆ Synopsis
A complete cubic Halin graph is a cubic Halin graph whose characteristic tree is a complete cubic tree, in which all leaves are at the same distance from the root vertex. In this work, we determine the strong chromatic index of the complete cubic Halin graph.
๐ SIMILAR VOLUMES
The strong chromatic index of a graph G, denoted sq(G), is the minimum number of parts needed to partition the edges of G into induced matchings. For 0 โค k โค l โค m, the subset graph S m (k, l) is a bipartite graph whose vertices are the kand l-subsets of an m element ground set where two vertices ar
## Abstract We show that a complete multipartite graph is class one if and only if it is not eoverfull, thus determining its chromatic index.
In this paper, we shall first prove that for a Halin graph G, 4 ยฐxT (G) ยฐ6, where x T (G) is the vertex-face total chromatic number of G. Second, we shall establish a sufficient condition for a Halin graph to have a vertex-face total chromatic number of 6. Finally, we shall give a necessary and suff
We show that the strong chromatic index of a graph with maximum degree 2 is at most (2&=) 2 2 , for some =>0. This answers a question of Erdo s and Nes etr il. 1997 Academic Press ## 1. Introduction A strong edge-colouring of a (simple) graph, G, is a proper edge-colouring of G with the added res