Bridge decompositions with distances at least two

Cyclic Labellings with Constraints at Two Distances

Motivated by problems in radio channel assignment, we consider the vertexlabelling of graphs with nonnegative integers. The objective is to minimize the span of the labelling, subject to constraints imposed at graph distances one and two. We show that the minimum span is (up to rounding) a piecewise linear function of the constraints, and give a complete specification, together with the associa...

Matroids with at least two regular elements

For a matroid M , an element e such that both M \ e and M/e are regular is called a regular element of M . We determine completely the structure of non-regular matroids with at least two regular elements. Besides four small size matroids, all 3-connected matroids in the class can be pieced together from F7 or S8 and a regular matroid using 3-sums. This result takes a step toward solving a probl...

Fitting Distances by Least Squares

Cubic graphs with total domatic number at least two

Let G be a graph. A total dominating set of G is a set S of vertices of G such that every vertex is adjacent to at least one vertex in S. The total domatic number of a graph is the maximum number of total dominating sets which partition the vertex set of G. In this paper we would like to characterize the cubic graphs with total domatic number at least two.

Packing paths of length at least two

We give a simple proof for Kaneko’s theorem which gives a su2cient and necessary condition for the existence of vertex disjoint paths in a graph, each of length at least two, that altogether cover all vertices of the original graph. Moreover we generalize this theorem and give a formula for the maximum number of vertices that can be covered by such a path system. c © 2004 Elsevier B.V. All righ...