A note on the existence of an alternating sign on a spanning tree of graphs

Details A note on the existence of an alternating sign on a spanning tree of graphs A note on the existence of an alternating sign on a spanning tree of graphs

2011-06-03

arxiv.org/abs/1106.0605v1

Mathematics

Combinatorics

Scientific paper

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.

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