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Minimum multiplicities of subgraphs and Hamiltonian systems

John Sheehan
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Abstract

Let G be a finite simple graph with automorphism group A(G). Then a spanning subgraph U of G is a fixing subgraph of G if G contains exactly $| A(G)|/ | A(G) \cap A(U)| $ subgraphs isomorphic to U: the graph G must always contain at least this number. If in addition $A(U) \subseteq A(G)$ then U is a strong fixing subgraph. Fixing subgraphs are important in many areas of graph theory. We consider them in the context of Hamiltonian graphs

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John Sheehan. 2000-12-28. Minimum multiplicities of subgraphs and Hamiltonian systems. https://arxiv.org/abs/math/0012258

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