Let G be a (p, q)-graph with edge domination number γ′ and edge domatic number d′. In this paper we characterize connected graphs for which γ′ = p/2 and graphs for which γ′ + d′ = q + 1. We also characterize trees and unicyclic graphs for which γ′ = bp/2c and γ′ = q −∆′, where ∆′ denotes the maximum degree of an edge in G.

This paper surveys some of the work that was inspired by Wagner’s general technique to prove completeness in the levels of the boolean hierarchy over NP and some related results. In particular, we show that it is DP-complete to decide whether or not a given graph can be colored with exactly four colors, where DP is the second level of the boolean hierarchy. This result solves a question raised ...

Consider the partition function S μ( ) associated in the theory of Rényi dimension to a finite Borel measure μ on Euclidean d-space. This partition function S μ( ) is the sum of the q-th powers of the measure applied to a partition of d-space into d-cubes of width . We further Guérin’s investigation of the relation between this partition function and the Lebesgue Lp norm (Lq norm) of the convol...

Consider the partition function S μ( ) associated in the theory of Rényi dimension to a finite Borel measure μ on Euclidean d-space. This partition function S μ( ) is the sum of the q-th powers of the measure applied to a partition of d-space into d-cubes of width . We further Guérin’s investigation of the relation between this partition function and the Lebesgue Lp norm (Lq norm) of the convol...