Self-Converse and Oriented Graphs among the Third Parts of Nearly Complete Digraphs

H

into t isomorphic parts is generalized so that either a remainder R or a surplus S, both of the numerically smallest possible size, are allowed. The sets of such nearly parts are defined to be the floor class and the ceiling class , respectively. We restrict ourselves to the case of nearly third parts of , the complete digraph, with . Then if , else and . The existence of nearly third parts which are oriented graphs and/or self-converse digraphs is settled in the affirmative for all or most n's. Moreover, it is proved that floor classes with distinct R's can have a common member. The corresponding result on the nearly third parts of the complete 2-fold graph is deduced. Furthermore, also if .

This is a preview of subscription content, access via your institution.

Author information

Affiliations

Authors

Additional information

Received: September 12, 1994/Revised: Revised November 3, 1995

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Meszka, M., Skupień, Z. Self-Converse and Oriented Graphs among the Third Parts of Nearly Complete Digraphs. Combinatorica 18, 413–424 (1998). https://doi.org/10.1007/PL00009830

Download citation

  • AMS Subject Classification (1991) Classes:  05C70, 05C20