Pairs Of Edges As Chords And As Cut-Edges

Pairs Of Edges As Chords And As Cut-Edges

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Several authors have studied the Remote Starter 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 Power Trunk Kit graphs, every two edges are always chords of a common cycle.