Channels, Billiards, and Perfect Matching 2-Divisibility

Perfect divisibility and 2-divisibility

A graph G is said to be 2-divisible if for all (nonempty) induced subgraphs H of G, V (H) can be partitioned into two sets A,B such that ω(A) < ω(H) and ω(B) < ω(H). A graph G is said to be perfectly divisible if for all induced subgraphs H of G, V (H) can be partitioned into two sets A,B such that H[A] is perfect and ω(B) < ω(H). We prove that if a graph is (P5, C5)-free, then it is 2-divisibl...

Srikumar 1 Perfect Matching and Matching Polytopes

Perfect Matching Preservers

For two bipartite graphs G and G , a bijection ψ : E(G) → E(G) is called a (perfect) matching preserver provided that M is a perfect matching in G if and only if ψ(M) is a perfect matching in G. We characterize bipartite graphs G and G which are related by a matching preserver and the matching preservers between them.

Perfect Matching Disclosure Attacks

Traffic analysis is the best known approach to uncover relationships amongst users of anonymous communication systems, such as mix networks. Surprisingly, all previously published techniques require very specific user behavior to break the anonymity provided by mixes. At the same time, it is also well known that none of the considered user models reflects realistic behavior which casts some dou...

The Polynomially Bounded Perfect Matching Problem Is in NC 2

The perfect matching problem is known to be in ¶, in randomized NC, and it is hard for NL. Whether the perfect matching problem is in NC is one of the most prominent open questions in complexity theory regarding parallel computations. Grigoriev and Karpinski [GK87] studied the perfect matching problem for bipartite graphs with polynomially bounded permanent. They showed that for such bipartite ...