By Alspach B., Xu M.Y.

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**Additional resources for 1/2-Transitive Graphs of Order 3p**

**Example text**

Edmonds, A combinatorial representation for polyhedral surfaces, Abstract in Notices Amer. Math. Soc. 7 (1960), 646. 6. M. Furst, J. L. Gross and L. McGeoch, Finding a maximum-genus graph imbedding, J. Assoc. Comp. Mach. 35 (1988), 523–534. 7. J. L. Gross, Voltage graphs, Discrete Math. 9 (1974), 239–246. 8. J. L. 4 of Handbook of Graph Theory, CRC Press, 2004. 32 Jonathan L. Gross and Thomas W. Tucker 9. J. L. Gross and S. R. Alpert, The topological theory of current graphs, J. Combin. Theory (B) 17 (1974), 218–233.

This direction of research has led to the recent exciting developments of the Graph Minor Theory (see Chapter 5). In this section, we develop Kuratowski-type theorems for maximum genus, starting with graphs of maximum genus 0. We note first that a 2-edge-connected graph G has maximum genus 0 if and only if G is a cycle. To see why, consider an ear decomposition P1 , P2 , · · ·, Pr of G. If G is not a cycle, then r > 1. Now it is easy to construct an embedding of genus 1 for the subgraph P1 ∪ P2 .

L. Gross and L. McGeoch, Finding a maximum-genus graph imbedding, J. Assoc. Comp. Mach. 35 (1988), 523–534. 7. J. L. Gross, Voltage graphs, Discrete Math. 9 (1974), 239–246. 8. J. L. 4 of Handbook of Graph Theory, CRC Press, 2004. 32 Jonathan L. Gross and Thomas W. Tucker 9. J. L. Gross and S. R. Alpert, The topological theory of current graphs, J. Combin. Theory (B) 17 (1974), 218–233. 10. J. L. Gross and M. L. Furst, Hierarchy for imbedding-distribution invariants of a graph, J. Graph Theory 11 (1987), 205–220.

### 1/2-Transitive Graphs of Order 3p by Alspach B., Xu M.Y.

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