Elsevier

Discrete Mathematics

Volume 212, Issues 1–2, 6 February 2000, Pages 129-139
Discrete Mathematics

On some third parts of nearly complete digraphs

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Abstract

For the complete digraph DKn with n⩾3, its half as well as its third (or near-third) part, both non-self-converse, are exhibited. A backtracking method for generating a tth part of a digraph is sketched. It is proved that some self-converse digraphs are not among the near-third parts of the complete digraph DK5 in four of the six possible cases. For n=9+6k,k=0,1,…, a third part D of DKn is found such that D is a self-converse oriented graph and all D-decompositions of DKn have trivial automorphism group.

Keywords

Graph
Multigraph
Digraph
Line decomposition
Floor
Ceiling
Self-converse
Isomorphic parts

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