Pairs of edge disjoint Hamiltonian circuits in 5-connected planar graphs.
Pairs Of Edges As Chords And As Cut-Edges
Several authors have studied the graphs for which every edge is a chord of a cycle; among 2-connected graphs, one characterization is that the deletion of one vertex never creates a cut-edge. Two new results: among 3-connected graphs with minimum degree at least 4, every two adjacent edges are chords of a common cycle if and only if deleting two vertices never creates two adjacent cut-edges; among 4-connected graphs, every two edges are always chords of a common cycle.
Parity versions of 2-connectedness.
Partition numbers, connectivity and Hamiltonicity
Partitionability of trees
Partitions of networks that are robust to vertex permutation dynamics
Minimum disconnecting cuts of connected graphs provide fundamental information about the connectivity structure of the graph. Spectral methods are well-known as stable and efficient means of finding good solutions to the balanced minimum cut problem. In this paper we generalise the standard balanced bisection problem for static graphs to a new “dynamic balanced bisection problem”, in which the bisecting cut should be minimal when the vertex-labelled graph is subjected to a general sequence of vertex...
Problemas aditivos y grafos de Cayley.