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arXiv · 2003.12960

The Erdős-Hajnal property for graphs with no fixed cycle as a pivot-minor

Jaehoon Kim·Sang-il Oum
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Abstract

We prove that for every integer $k$, there exists $\varepsilon > 0$ such that for every n-vertex graph $G$ with no pivot-minor isomorphic to $C_k$, there exist disjoint sets $A,B \subseteq V(G)$ such that $|A|,|B| \geq \varepsilon n$, and $A$ is either complete or anticomplete to $B$. This proves the analog of the Erdős-Hajnal conjecture for the class of graphs with no pivot-minor isomorphic to $C_k$.

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BibTeXRIS

Jaehoon Kim, Sang-il Oum. 2021-07-01. The Erdős-Hajnal property for graphs with no fixed cycle as a pivot-minor. https://doi.org/10.37236/9536

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