SOME PROPERTIES OF THE INCOMPLETE ARC TOURNAMENTS THAT DO NOT HAVE DISJOINT CYCLES OF DIFFERENT
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DOI:
https://doi.org/10.34238/tnu-jst.15509Abstract
The problem of studying the existence of disjoint cycles in directed graphs has been studied since 1983 by C. Thomassen. In 2012, Henning and Yeo extended the problem by studying the existence of disjoint cycles of different lengths in directed graphs. To date, this problem has yielded many profound and interesting results for different classes of graphs, notablytournaments, k-part tournaments, local tournaments, etc. In this paper, we will continue to study the existence of disjoint cycles of different lengths for the class of incomplete arc tournaments (which can be considered an extension of the class of tournaments). The main result is the proof of several important properties of the class of incomplete arc tournaments when they are strongly connected, have a minimum degree of 3, and do not have disjoint cycles of different lengths.Downloads
References
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