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Special subdivisions ofK 4 and 4-chromatic graphs

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Abstract

In this paper we consider special subdivisions ofK 4 in which some of the edges are left undivided. A best possible extremal-result for the case where the edges of a Hamiltonian path are left undivided is obtained. Moreover special subdivisions as subgraphs of 4-chromatic graphs are studied. Our main-result on 4-chromatic graphs says that any 4-critical graphG contains an odd cycleC without diagonals such thatG-V (C) is connected.

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Authors and Affiliations

  1. Department of Mathematics, University of Odense, DK-5320, Odense M., Denmark

    Uffe Krusenstjerna-Hafstrøm &  Bjarne Toft

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  1. Uffe Krusenstjerna-Hafstrøm
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  2. Bjarne Toft
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Krusenstjerna-Hafstrøm, U., Toft, B. Special subdivisions ofK 4 and 4-chromatic graphs. Monatshefte für Mathematik 89, 101–109 (1980). https://doi.org/10.1007/BF01476588

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  • DOI: https://doi.org/10.1007/BF01476588

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