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arXiv · 1710.07546

Sum-perfect graphs

Bart Litjens·Sven Polak·Vaidy Sivaraman
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Abstract

Inspired by a famous characterization of perfect graphs due to Lovász, we define a graph $G$ to be sum-perfect if for every induced subgraph $H$ of $G$, $α(H) + ω(H) \geq |V(H)|$. (Here $α$ and $ω$ denote the stability number and clique number, respectively.) We give a set of $27$ graphs and we prove that a graph $G$ is sum-perfect if and only if $G$ does not contain any of the graphs in the set as an induced subgraph.

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Bart Litjens, Sven Polak, Vaidy Sivaraman. 2017-10-20. Sum-perfect graphs. https://doi.org/10.1016/j.dam.2018.12.015

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