|Title:||A note on the Gallai-Roy-Vitaver Theorem||Authors:||Chang, Gerard-J.
|Keywords:||Coloring;k-Coloring;Chromatic number;Path;Tournament||Issue Date:||2002||Start page/Pages:||441-444||Source:||Discrete mathematics 256||Abstract:||
The well-known theorem by Gallai–Roy–Vitaver says that every digraph G has a directed
path with at least X(G) vertices; hence this holds also for graphs. Li strengthened the digraph
result by showing that the directed path can be constrained to start from any vertex that can
reach all others. For a graph G given a proper X(G)-coloring, he proved that the path can be
required to start at any vertex & visit vertices of all colors. We give a shorter proof of this. He
conjectured that the same holds for digraphs; we provide a strongly connected counterexample.
We also give another extension of the Gallai–Roy–Vitaver Theorem on graphs.
|Appears in Collections:||數學系|
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