A note on the double-critical graph conjecture
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چکیده
A connected n-chromatic graph G is double-critical if for all the edges xy of G, the graph G−x−y is (n−2)-chromatic. In 1966, Erdős and Lovász conjectured that the only double-critical n-chromatic graph is Kn. This conjecture remains unresolved for n ≥ 6. In this short note, we verify this conjecture for claw-free graphs G of chromatic number 6.
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