Let G = (V(G), E(G)) be a graph. A set S ⊆ E(G) is an edge k-cut in G if the graph G − S = (V(G), E(G) \ S) has at least k connected components. The generalized k-edge connectivity of a graph G, ...

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 ...

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 ...