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On the ultimate normalized chromatic difference sequence of a graph

โœ Scribed by Huishan Zhou

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
489 KB
Volume
148
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

โœฆ Synopsis

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 difference sequence cds (G)

๐Ÿ“œ SIMILAR VOLUMES

The chromatic difference sequence of the
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โœ Huishan Zhou ๐Ÿ“‚ Article ๐Ÿ“… 1991 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 953 KB

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

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The harmonious chromatic number of a graph G, denoted by h(G), is the least number of colon which can be assigned to the vertices of G such that adjacent vertices are colored differently and any two distinct edges have different color pairs. This is a slight variation of a definition given independe

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โœ Paul A. Catlin ๐Ÿ“‚ Article ๐Ÿ“… 1978 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 392 KB

We give an upper bound on the chromatic number of a graph in terms of its maximum degree and the size of the largest complete subgraph. Our result extends a theorem due to i3rook.s.

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Let C be a simple graph. let JiGI denote the maximum degree of it\ \erlicek. ,III~ Ic~r \ 1 C; 1 denote irs chromatic pumber. Brooks' Theorem asserb lha1 ytG I'--AI G I. unk\\ C; hd.. .I component that is a COI lplete graph K,,,,\_ ,. or ullesq .I1 G I = 2 and G ha\ ;~n c~rld C\CIC