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The Existence of an Alternating Sign on a Spanning Tree of Graphs

Kim, Dongseok;Kwon, Young Soo;Lee, Jaeun

  • Received : 2012.01.28
  • Accepted : 2012.09.24
  • Published : 2012.12.23

Abstract

For a spanning tree T of a connected graph ${\Gamma}$ and for a labelling ${\phi}$: E(T) ${\rightarrow}$ {+,-},${\phi}$ is called an alternating sign on a spanning tree T of a graph ${\Gamma}$ if for any cotree edge $e{\in}E({\Gamma})-E(T)$, the unique path in T joining both end vertices of e has alternating signs. In the present article, we prove that any graph has a spanning tree T and an alternating sign on T.

Keywords

bipartite graphs;induced graphs;spanning trees;alternating signs;Seifert surfaces

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Cited by

  1. THE BOUNDARIES OF DIPOLE GRAPHS AND THE COMPLETE BIPARTITE GRAPHS K2,n vol.36, pp.2, 2014, https://doi.org/10.5831/HMJ.2014.36.2.399

Acknowledgement

Supported by : Korea Science and Engineering Foundation