Edge colouring is a fundamental concept in graph theory whereby colours are assigned to the edges of a graph such that no two adjacent edges share the same colour. This process is central to numerous ...

In this paper, motivated by the study of the wide diameter and the Rabin number of graphs, we define the generalized k-diameter of k-connected graphs, and show that every k-regular k-connected graph ...

SIAM Journal on Applied Mathematics, Vol. 26, No. 2 (Mar., 1974), pp. 313-314 (2 pages) A very short new constructive proof is presented of a result of Edmond's that a set of degrees each at least k ...

Let r 2 be a real number and let G be a graph and D an orientation of its edges. A function f: E(G) R is a nowhere-zero circular r-flow if for every vertex v of G, the sum of the f-values on the ...

Conjecture 1 (Tutte [2]): If G is a 2-edge-connected graph, then G admits a nowhere-zero 5-flow. If true, Conjecture 1 would imply that for every integer k > 4, the flow polynomial of any ...