1 research outputs found
Largest 2-regular subgraphs in 3-regular graphs
For a graph , let denote the largest number of vertices in a
-regular subgraph of . We determine the minimum of over
-regular -vertex simple graphs . To do this, we prove that every
-regular multigraph with exactly cut-edges has a -regular subgraph
that omits at most vertices. More generally,
every -vertex multigraph with maximum degree and edges has a
-regular subgraph that omits at most vertices. These bounds are sharp; we describe the
extremal multigraphs