The edges of the Cartesian product of graphs G x H a r e to be colored with the condition that all rectangles, i.e., K2 x K2 subgraphs, must be colored with four distinct colors. The minimum number of colors in such colorings is determined for all pairs of graphs except when G is 5-chromatic and H
Investigations on an edge coloring problem
β Scribed by D. de Werra
- Book ID
- 107748111
- Publisher
- Elsevier Science
- Year
- 1971
- Tongue
- English
- Weight
- 527 KB
- Volume
- 1
- Category
- Article
- ISSN
- 0012-365X
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## Abstract When can a __k__βedgeβcoloring of a subgraph __K__ of a graph __G__ be extended to a __k__βedgeβcoloring of __G__? One necessary condition is that for all __X β E__(__G__) β __E__(__K__), where ΞΌ~i~(__X__) is the maximum cardinality of a subset of __X__ whose union with the set of edg
An edge-coloring of a simple graph \(G\) with colors \(1,2, \ldots, t\) is called an interval \(t\)-coloring [3] if at least one edge of \(G\) is colored by color \(i, i=1, \ldots, t\) and the edges incident with each vertex \(x\) are colored by \(d_{G}(x)\) consecutive colors, where \(d_{G}(x)\) is