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The nonadditivity of the genus

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Abstract

A class of cubic graphs is introduced for which the genus is a nonadditive function of the genus of subgraphs. This provides a small (28 node) counterexample to Duke’s conjecture concerning the relation of the Betti number to the genus of a graph.

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References

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    Martin Milgram

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  1. Martin Milgram
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Milgram, M. The nonadditivity of the genus. Israel J. Math. 19, 201–207 (1974). https://doi.org/10.1007/BF02757712

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  • DOI: https://doi.org/10.1007/BF02757712

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