A counterexample is presented to Gy. Elekes's conjecture concerning the existence of long 2-colored paths in properly colored graphs. A modified version of the conjecture is ...
The currently (asymptotically) fastest algorithm for minimum dominating set on graphs of n nodes is the trivial (2n) algorithm which enumerates and checks all the subsets of
Consider a connected r-regular n-vertex graph G with random independent edge lengths, each uniformly distributed on [0, 1]. Let mst(G) be the expected length of a minimum spanning...
A block graph is a graph whose blocks are cliques. A block duplicate (BD) graph is a graph obtained by adding true twins (i.e., adjacent vertices with the same closed neighborhood...
The bandwidth minimization problem has a long history and a number of practical applications. In this paper we introduce a natural extension of bandwidth to partially ordered layo...