For graphs G and H, the Cartesian product G ร H is defined as follows: the vertex set is ## V(G) ร V(H), and two vertices (g,h) and (9',h') are adjacent in G ร H if either g = g' and hh' E E(H) or h = h' and g9' E E(G). Let G k denote the Cartesian product of k copies of G. The chromatic differen
The chromatic difference sequence of a graph
โ Scribed by Michael O Albertson; David M Berman
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 713 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Zhou, H., The chromatic difference sequence of the Cartesian product of graphs, Discrete Mathematics 90 (1991) 297-311. The chromatic difference sequence cds(G) of a graph G with chromatic number n is defined by cds(G) = (a(l), a(2), . . , a(n)) if the sum of a(l), a(2), . , a(t) is the maximum numb
Let n, 2 n2 L . . B n, 2 2 be integers. We say that G has an (n,, n2, , . , , n,)-chromatic factorization if G can be edge-factored as G, @ G2 @ + . . @ G, with x ( G , ) = n,, for i = 1,2, . . . , k . The following results are proved : then K,, has an (n,, n2,, . , , n,)-chromatic factorization. W
## Abstract We study a generalization of the notion of the chromatic number of a graph in which the colors assigned to adjacent vertices are required to be, in a certain sense, far apart. ยฉ 1993 John Wiley & Sons, Inc.
Following [1] , we investigate the problem of covering a graph G with induced subgraphs G 1 ; . . . ; G k of possibly smaller chromatic number, but such that for every vertex u of G, the sum of reciprocals of the chromatic numbers of the G i 's containing u is at least 1. The existence of such ''ch
We define a skew edge coloring of a graph to be a set of two edge colorings such that no two edges are assigned the same unordered pair of colors. The skew chromatic index s(G) is the minimum number of colors required for a skew edge coloring of G. We show that this concept is closely related to tha