Lower bound of the hadwiger number of graphs by their average degree

Combinatorica volume 4, pages307–316(1984)Cite this article

Abstract

The aim of this paper is to show that the minimum Hadwiger number of graphs with average degreek isO(k/√logk). Specially, it follows that Hadwiger’s conjecture is true for almost all graphs withn vertices, furthermore ifk is large enough then for almost all graphs withn vertices andnk edges.

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Affiliations

  1. Mathematical Institute of the Siberian Branch of the, Soviet Academy of Sciences, Novosibirsk-90, 630090, U.S.S.R.

    A. V. Kostochka

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  1. A. V. Kostochka
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Kostochka, A.V. Lower bound of the hadwiger number of graphs by their average degree. Combinatorica 4, 307–316 (1984). https://doi.org/10.1007/BF02579141

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AMS subject classification 1980)

  • 05 C 10
  • 05 C 15
  • 60 C 05