Perfect matchings after vertex deletions

Perfect matchings after vertex deletions

This paper considers some classes of graphs which are easily seen to have many perfect matchings. Such graphs can be considered robust with respect to the property of having a perfect matching if under vertex deletions (with some mild restrictions), the resulting subgraph continues to have a perfect matching. It is clear that you can destroy the property of having a perfect matching by deleting...

Perfect Matchings in Grid Graphs after Vertex Deletions

Vertex Degree Sums for Perfect Matchings in 3-uniform Hypergraphs

We determine the minimum degree sum of two adjacent vertices that ensures a perfect matching in a 3-graph without isolated vertex. More precisely, suppose that H is a 3-uniform hypergraph whose order n is sufficiently large and divisible by 3. If H contains no isolated vertex and deg(u)+deg(v) > 2 3 n2− 8 3 n+2 for any two vertices u and v that are contained in some edge of H, then H contains a...

Approximated Vertex Cover for Graphs with Perfect Matchings

Chen and Kanj considered the V C problem for graphs with perfect matchings (VC-PM). They showed that: (i) There is a reduction from general V C to VC-PM, which guarantees that if one can achieve an approximation factor of less than two for VC-PM, then one can do so for general V C as well. (ii) There is an algorithm for VC-PM whose approximation factor is given as 1.0...

Perfect Matchings in Edge-Transitive Graphs

We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...