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

• Journal title : Kyungpook mathematical journal
• Volume 52, Issue 4,  2012, pp.513-519
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2012.52.4.513
Title & Authors
The Existence of an Alternating Sign on a Spanning Tree of Graphs
Kim, Dongseok; Kwon, Young Soo; Lee, Jaeun;

Abstract
For a spanning tree T of a connected graph $\small{{\Gamma}}$ and for a labelling $\small{{\phi}}$: E(T) $\small{{\rightarrow}}$ {+,-},$\small{{\phi}}$ is called an alternating sign on a spanning tree T of a graph $\small{{\Gamma}}$ if for any cotree edge $\small{e{\in}E({\Gamma})-E(T)}$, 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;
Language
English
Cited by
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THE BOUNDARIES OF DIPOLE GRAPHS AND THE COMPLETE BIPARTITE GRAPHS K2,n,;

호남수학학술지, 2014. vol.36. 2, pp.399-415
1.
THE BOUNDARIES OF DIPOLE GRAPHS AND THE COMPLETE BIPARTITE GRAPHS K2,n, Honam Mathematical Journal, 2014, 36, 2, 399
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