On the P4-structure of perfect graphs III. Partner decompositions
✍ Scribed by V Chvátal
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 243 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
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Given a graph G we define its k-overlap graph as the graph whose vertices are the induced P 4 's of G and two vertices in the overlap graph are adjacent if the corresponding P 4 's in G have exactly k vertices in common. For k=1, 2, 3 we prove that if the k-overlap graph of G is bipartite then G is
## Abstract Generalizing the well‐known concept of an __i__‐perfect cycle system, Pasotti [Pasotti, in press, Australas J Combin] defined a Γ‐decomposition (Γ‐factorization) of a complete graph __K__~__v__~ to be __i‐perfect__ if for every edge [__x__, __y__] of __K__~__v__~ there is exactly one bl