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Perfect graphs with unique P4-structure

✍ Scribed by Stefan Hougardy


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
635 KB
Volume
165-166
Category
Article
ISSN
0012-365X

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✦ Synopsis


We will extend Reed's Semi-Strong Perfect Graph Theorem by proving that unbreakable c'ifree graphs different from a Ce and its complement have unique Ph-structure.


πŸ“œ SIMILAR VOLUMES


On theP4-Structure of Perfect Graphs V.
✍ ChΔ±́nh T. HoΓ ng; Stefan Hougardy; FrΓ©dΓ©ric Maffray πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 480 KB

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

Large P4-free graphs with bounded degree
✍ Myung S. Chung; Douglas B. West πŸ“‚ Article πŸ“… 1993 πŸ› John Wiley and Sons 🌐 English βš– 424 KB

## Abstract Let __ex__ \* (__D__; __H__) denote the maximum number of edges in a connected graph with maximum degree __D__ and no induced subgraph isomorphic to __H.__ We prove that this is finite only when __H__ is a disjoint union of paths,m in which case we provide crude upper and lower bounds.