Abstract
A kernel in a digraph is a set of vertices that is both an absorbing and independent set. In [4] P. Duchet conjectured that a digraph such that every odd circuit has two short chords is kernel perfect digraph (i.e. every induced subdigraph has a kernel) and he proved the conjecture for digraphs where every 3 -circuit is reversal. We give another simple proof of this result by using reorientation and constructive methods. We also show that the conjecture is valid for digraphs D where the underlying undirected spanning subgraph deduced from the spanning subdigraph of D with only pairs of symmetric arcs is a comparability graph.
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More From: AKCE International Journal of Graphs and Combinatorics
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