We determine the asymptotic behaviour of the number of eulerian circuits in a complete graph of odd order. One corollary of our result is the following. If a maximum random walk, ...
We prove the conjecture of Abbott and Katchalski that for every m ≥ 2 there is a positive constant λm such that S(Kd mn) ≥ λmnd−1 S(Kd−1 m ) where S(Kd m) is the length o...
The distinguishing number D(G) of a graph G is the least integer d such that G has a labeling with d labels that is preserved only by a trivial automorphism. We prove that Cartesi...
Let ccl(G) denote the order of the largest complete minor in a graph G (also called the contraction clique number) and let Gn,p denote a random graph on n vertices with edge probab...
We study the graph partitioning problem on ddimensional ball graphs in a geometric way. Let B be a set of balls in d-dimensional Euclidean space with radius ratio and -precision....