For any simple graph G, Vizing's Theorem [5] implies that A (G)~)((G)<~ A(G)+ 1, where A (G) is the maximum degree of a vertex in G and x(G) is the edge chromatic number. It is of course possible to add edges to G without changing its edge chromatic number. Any graph G is a spanning subgraph of an e
Dynamic chromatic number of regular graphs
β Scribed by Meysam Alishahi
- Book ID
- 116401289
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 222 KB
- Volume
- 160
- Category
- Article
- ISSN
- 0166-218X
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π SIMILAR VOLUMES
## Abstract We determine the minimum number of edges in a regular connected graph on __n__ vertices, containing a complete subgraph of order __k__ β€ __n__/2. This enables us to confirm and strengthen a conjecture of P. ErdΓΆs on the existence of regular graphs with prescribed chromatic number.
## Abstract The __r__βacyclic edge chromatic number of a graph is defined to be the minimum number of colors required to produce an edge coloring of the graph such that adjacent edges receive different colors and every cycle __C__ has at least min(|__C__|, __r__) colors. We show that (__r__βββ2)__d