We show that the intersection graph of a collection of subsets of the plane, where each subset forms an "L" shape whose vertical stem is infinite, has its chromatic number 1 bounded by a function of the order of its largest clique w, where it is shown that ;1<2"4'3"4"'~'-". This proves a special cas
On the structure of graphs with bounded asteroidal number
✍ Scribed by T. Kloks; D. Kratsch; H. Müller
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 13 KB
- Volume
- 3
- Category
- Article
- ISSN
- 1571-0653
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
The bondage number b(G) of a graph G is the minimum cardinality of a set of edges of G whose removal from G results in a graph with domination number larger than that of G. Several new sharp upper bounds for b(G) are established. In addition, we present an infinite class of graphs each of whose bond
The k-domination number of a graph is the cardinality of a smallest set of vertices such that every vertex not in the set is adjacent to at least k vertices of the set. We prove two bounds on the k-domination number of a graph, inspired by two conjectures of the computer program Graffiti.pc. In part
Let G be a simple graph of order n such that every vertex of degree 1 is adjacent to a vertex of degree at least 3. In this work, we prove that the line graph L(G) has a 2-factor with at most n-1 3 components if every odd branch-bond of G has a shortest branch of length 2. This is a best possible re
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
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.