Matchings in m-generalized fullerene graphs

Generalized subgraph-restricted matchings in graphs

For a graph property P, we define a P-matching as a set M of disjoint edges such that the subgraph induced by the vertices incident to M has property P. Previous examples include strong/induced matchings and uniquely restricted matchings. We explore the general properties of P-matchings, but especially the cases where P is the property of being acyclic or the property of being disconnected. We ...

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...

On Negative Dependency Graphs in Spaces of Generalized Random Matchings

Matchings in Graphs

LP relaxation One way to deal with this is to relax the integrality constraints and allow xe ∈ [0, 1] to get a linear program, which can be solved in polynomial-time. However, this gives rise to fractional matchings. Characteristic vectors of matchings in G can be seen as points in R where m = |E|. The convex hull of all the matchings forms a polytope called the matching polytope M. However, th...

Matchings in Geometric Graphs

A geometric graph is a graph whose vertex set is a set of points in the plane and whose edge set contains straight-line segments. A matching in a graph is a subset of edges of the graph with no shared vertices. A matching is called perfect if it matches all the vertices of the underling graph. A geometric matching is a matching in a geometric graph. In this thesis, we study matching problems in...