Parallel Algorithms for Finding a Hamiltonian Path and a Hamiltonian Cycle in an In-Tournament Graph

Shin-ichi NAKAYAMA  Shigeru MASUYAMA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E81-A   No.5   pp.757-767
Publication Date: 1998/05/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
parallel algorithms,  Hamiltonian path,  Hamiltonian cycle,  in-tournament,  

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As a super class of tournament digraphs, Bang-Jensen, Huang and Prisner defined an in-tournament digraph (in-tournament for short) and investigated a number of its nice properties. The in-tournament is a directed graph in which the set of in-neighbors of every vertex induces a tournament digraph. In other words, the presence of arcs (x,z) and (y,z) implies that exactly one of (x,y) or (y,x) exists. In this paper, we propose, for in-tournaments, parallel algorithms for examining the existence of a Hamiltonian path and a Hamiltonian cycle and for constructing them, if they exist.