Simplicial Vertices in Graphs with no Induced Four‐Edge Path or Four‐Edge Antipath,and the H6‐Conjecture |
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Authors: | Maria Chudnovsky Peter Maceli |
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Affiliation: | DEPARTMENT OF IEOR COLUMBIA UNIVERSITY, NEW YORK, NY |
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Abstract: | Let be the class of all graphs with no induced four‐edge path or four‐edge antipath. Hayward and Nastos 6 conjectured that every prime graph in not isomorphic to the cycle of length five is either a split graph or contains a certain useful arrangement of simplicial and antisimplicial vertices. In this article, we give a counterexample to their conjecture, and prove a slightly weaker version. Additionally, applying a result of the first author and Seymour 1 we give a short proof of Fouquet's result 3 on the structure of the subclass of bull‐free graphs contained in . |
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Keywords: | induced subgraph path antipath |
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