Israel Journal of Mathematics

, Volume 19, Issue 3, pp 201–207 | Cite as

The nonadditivity of the genus

  • Martin Milgram


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.


Planar Graph Additive Function Previous Lemma Betti Number Free Edge 
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Copyright information

© Hebrew University 1975

Authors and Affiliations

  • Martin Milgram
    • 1
  1. 1.Silver SpringU.S.A.

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