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2020•arXiv (Cornell University)Open access

A note on the largest induced matching in graphs avoiding a fixed bipartite graph

Ben Lund, Daniel Reichman

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Abstract

We give a simple proof that every $n$-vertex graph $d$-regular graph that does not contain a fixed bipartite graph as a subgraph has an induced matching of size $Ω((n/d)(\log d))$.

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What this paper is about

We give a simple proof that every $n$-vertex graph $d$-regular graph that does not contain a fixed bipartite graph as a subgraph has an induced matching of size $Ω((n/d)(\log d))$.

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Available abstract

We give a simple proof that every $n$-vertex graph $d$-regular graph that does not contain a fixed bipartite graph as a subgraph has an induced matching of size $Ω((n/d)(\log d))$.

Key concepts: Bipartite graph, Combinatorics, Factor-critical graph, Mathematics, Distance-hereditary graph, Matching (statistics), Line graph, Graph

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