## Abstract Both the line graph and the clique graph are defined as intersection graphs of certain families of complete subgraphs of a graph. We generalize this concept. By a __k__βedge of a graph we mean a complete subgraph with __k__ vertices or a clique with fewer than __k__ vertices. The __k__β
A polynomial algorithm for constructing the clique graph of a line graph
β Scribed by Bruce Hedman
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 250 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0166-218X
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π SIMILAR VOLUMES
Discrete Mathematics 3X ( 19X2) 6S-71 North-Holland Publishing Company 65 Let G = (V, E) be a graph with a positive number wt(v) assigned to each L' E V. A weighted clique saver of the vertices of G is a collection of cliques with a non-negative weight yC. assigned to each clique C in the collection
## 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.
Let G be a line graph. Orlin determined the clique covering and clique partition numbers cc(G) and cp(G). We obtain a constructive proof of Orlin's result and in doing so we are able to completely enumerate the number of distinct minimal clique covers and partitions of G, in terms of easily calculab
## 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