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- W2950277564 abstract "For a graph $G$, let $f_2(G)$ denote the largest number of vertices in a $2$-regular subgraph of $G$. We determine the minimum of $f_2(G)$ over $3$-regular $n$-vertex simple graphs $G$. To do this, we prove that every $3$-regular multigraph with exactly $c$ cut-edges has a $2$-regular subgraph that omits at most $max{0,lfloor (c-1)/2rfloor}$ vertices. More generally, every $n$-vertex multigraph with maximum degree $3$ and $m$ edges has a $2$-regular subgraph that omits at most $max{0,lfloor (3n-2m+c-1)/2rfloor}$ vertices. These bounds are sharp; we describe the extremal multigraphs." @default.
- W2950277564 created "2019-06-27" @default.
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- W2950277564 date "2019-03-21" @default.
- W2950277564 modified "2023-09-23" @default.
- W2950277564 title "Largest 2-regular subgraphs in 3-regular graphs" @default.
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