Improvements of the theorem of Duchet and Meyniel on Hadwiger's conjecture
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چکیده
منابع مشابه
Improvements of the theorem of Duchet and Meyniel on Hadwiger's conjecture
Probably the best-known among the remaining unsolved problems in graph theory is Hadwiger’s Conjecture: If χ(G) denotes the chromatic number of graph G, then G has the complete graph Kχ(G) as a minor. The following would immediately follow from the truth of Hadwiger’s Conjecture: Conjecture: If G has n vertices and if α(G) denotes the independence number of G, then G has Kdn/α(G)e as a minor. I...
متن کاملA basic elementary extension of the Duchet-Meyniel theorem
The Conjecture of Hadwiger implies that the Hadwiger number h times the independence number α of a graph is at least the number of vertices n of the graph. In 1982 Duchet and Meyniel proved a weak version of the inequality, replacing the independence number α by 2α− 1, that is, (2α− 1) · h ≥ n. In 2005 Kawarabayashi, Plummer and the second author published an improvement of the theorem, replaci...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2005
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2005.04.001