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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Graphs with the circuit cover property
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by Brian Alspach, Luis Goddyn and Cun Quan Zhang PDF
Trans. Amer. Math. Soc. 344 (1994), 131-154 Request permission

Abstract:

A circuit cover of an edge-weighted graph (G, p) is a multiset of circuits in G such that every edge e is contained in exactly $p(e)$ circuits in the multiset. A nonnegative integer valued weight vector p is admissible if the total weight of any edge-cut is even, and no edge has more than half the total weight of any edge-cut containing it. A graph G has the circuit cover property if (G, p) has a circuit cover for every admissible weight vector p. We prove that a graph has the circuit cover property if and only if it contains no subgraph homeomorphic to Petersen’s graph. In particular, every 2-edge-connected graph with no subgraph homeomorphic to Petersen’s graph has a cycle double cover.
References
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 344 (1994), 131-154
  • MSC: Primary 05C38; Secondary 05C70
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1181180-1
  • MathSciNet review: 1181180