Local tournaments and proper circular arc graphs
A local tournament is a digraph in which the out-set as well as the in-set of every vertex is a tournament. These digraphs have recently been found to share many desirable properties of tournaments. We illustrate this by giving O(m+n logn) algorithms to find a hamiltonian path and cycle in a local tournament. We mention several characterizations and recognition algorithms of graphs orientable as local tournaments. It turns out that they are precisely the graphs previously studied as proper circular arc graphs. Thus we obtain new recognition algorithms for proper circular arc graphs. We also give a more detailed structural characterization of chordal graphs that are orientable as local tournaments, i.e., that are proper circular arc graphs.
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