Fork-forests in bi-colored complete bipartite graphs
Motivated by the problem in (Tveretina etal., 2009)[8], which studies problems from propositional proof complexity, 2 2 -edge colorings of complete bipartite graphs are investigated. It is shown that if the edges of G=Kn,n G = K n , n are colored with black and white such that the number of black edges differs from the number of white edges by at most 1 1 , then there are at least n ( 1 ? 1 / 2 ) vertex-disjoint forks with centers in the same partite set of G G . Here, a fork is a graph formed by two adjacent edges of different colors. The bound is sharp. Moreover, an algorithm running in time O ( n 2 log n n ? ( n 2 , n ) log n ) and giving a largest such fork forest is found.
bi-colored star forests balanced colorings obdd