## Abstract Chung (F. R. K. Chung, On the decomposition of graphs, __SIAM J. Algebraic Discrete Methods__ 23 (1981), 1β12.) and independently GyΓΆri and Kostochka (E. GyΓΆri and A. V. Kostochka, On a problem of G. O. H. Katona and T. TarjΓ‘n, __Acta Math. Acad. Sci. Hung.__ 34 (1979), 321β327.) proved
The greedy clique decomposition of a graph
β Scribed by Sean McGuinness
- Publisher
- John Wiley and Sons
- Year
- 1994
- Tongue
- English
- Weight
- 181 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
We prove that if maximal cliques are removed one by one from any graph with n vertices, then the graph will be empty after at most n^2^/4 steps. This proves a conjecture of Winkler.
π SIMILAR VOLUMES
## Abstract A graph is point determining if distinct vertices have distinct neighborhoods. The nucleus of a pointβdetermining graph is the set __G__^O^ of all vertices, __v__, such that __G__β__v__ is point determining. In this paper we show that the size, Ο(__G__), of a maximum clique in __G__ sat
## SUM MARY An efficient algorithm is developed for the formation of a minimal cycle basis of a graph. This method reduces the number of cycles to be considered as (candidates for being the elements of a minimal basis and makes practical use of the Greedy algorithm feasible. A comparison is made b
## Abstract We produce in this paper an upper bound for the number of vertices existing in a clique of maximum cardinal. The proof is based in particular on the existence of a maximum cardinal clique that contains no vertex __x__ such that the neighborhood of __x__ is contained in the neighborhood