A note on the existence of an alternating sign on a spanning tree of graphs
Combinatorics
2013-02-18 v1 Geometric Topology
Abstract
For a spanning tree T of a connected graph G and for a labelling \phi: E(T) \rightarrow {+, -}, \phi is called an alternating sign on a spanning tree T of a graph G if for any cotree edge e \in E(G)-E(T), the unique path in T joining both end vertices of e has alternating signs. In the present note, we prove that any graph has a spanning tree T and an alternating sign on T.
Cite
@article{arxiv.1106.0605,
title = {A note on the existence of an alternating sign on a spanning tree of graphs},
author = {Dongseok Kim and Young Soo Kwon and Jaeun Lee},
journal= {arXiv preprint arXiv:1106.0605},
year = {2013}
}