We consider the variant of the minimum vertex cover problem in which we require that the cover induces a connected subgraph. We give new approximation results for this problem in d...
This paper addresses the following questions for a given tree T and integer d 2: (1) What is the minimum number of degree-d subtrees that partition E(T)? (2) What is the minimum n...
A biclique is a complete bipartite subgraph of a graph. This paper investigates the fractional biclique cover number, bc(G), and the fractional biclique partition number, bp(G), o...
We introduce a new notion of minors for simplicial complexes (hypergraphs), so-called homological minors. Our motivation is to propose a general approach to attack certain extrema...
Abstract. We outline a general theory of graph polynomials which covers all the examples we found in the vast literature, in particular, the chromatic polynomial, various generaliz...