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|Abstract:||The ErdAs-Hajnal conjecture states that for every graph H, there exists a constant delta(H)> 0, such that if a graph G has no induced subgraph isomorphic to H, then G contains a clique or a stable set of size at least |V (G)| (delta(H)). This conjecture is still open. We consider a variant of the conjecture, where instead of excluding H as an induced subgraph, both H and H (c) are excluded. We prove this modified conjecture for the case when H is the five-edge path. Our second main result is an asymmetric version of this: we prove that for every graph G such that G contains no induced six-edge path, and G (c) contains no induced four-edge path, G contains a polynomial-size clique or stable set.|
|Electronic Publication Date:||5-Aug-2014|
|Citation:||Chudnovsky, Maria, Seymour, Paul. (2015). Excluding paths and antipaths. COMBINATORICA, 35 (389 - 412. doi:10.1007/s00493-014-3000-z|
|Pages:||389 - 412|
|Type of Material:||Journal Article|
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