𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The greedy clique decomposition of a graph

✍ 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.

✦ 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.


πŸ“œ SIMILAR VOLUMES


An algorithm for the decomposition of gr
✍ Xiang-Ying Su πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 340 KB πŸ‘ 1 views

## Abstract Chung (F. R. K. Chung, On the decomposition of graphs, __SIAM J. Algebraic Discrete Methods__ 23 (1981), 1–12.) 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), 321–327.) proved

An upper bound on the size of a largest
✍ Dennis P. Geoffroy; David P. Sumner πŸ“‚ Article πŸ“… 1978 πŸ› John Wiley and Sons 🌐 English βš– 308 KB πŸ‘ 1 views

## Abstract A graph is point determining if distinct vertices have distinct neighborhoods. The nucleus of a point‐determining graph is the set __G__^O^ of all vertices, __v__, such that __G__–__v__ is point determining. In this paper we show that the size, Ο‰(__G__), of a maximum clique in __G__ sat

Revised Greedy algorithm for formation o
✍ Kaveh, A. ;Roosta, G. R. πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 356 KB πŸ‘ 1 views

## 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

An upper bound on the size of the larges
✍ Alain Billionnet πŸ“‚ Article πŸ“… 1981 πŸ› John Wiley and Sons 🌐 English βš– 194 KB πŸ‘ 1 views

## 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