Counting the spanning trees of the 3-cube using edge slides

zbMATH Open1278.05075arXiv1109.6393MaRDI QIDQ2869470

Christopher Tuffley

Publication date: 3 January 2014

Published in: The Australasian Journal of Combinatorics (Search for Journal in Brave)

Abstract: We give a direct combinatorial proof of the known fact that the 3-cube has 384 spanning trees, using an "edge slide" operation on spanning trees. This gives an answer in the case n=3 to a question implicitly raised by Stanley. Our argument also gives a bijective proof of the n=3 case of a weighted count of the spanning trees of the n-cube due to Martin and Reiner.

Full work available at URL: https://arxiv.org/abs/1109.6393

Mathematics Subject Classification ID

Trees (05C05) Enumeration in graph theory (05C30)

Related Items (1)

Characterisation and classification of signatures of spanning trees of the $n$-cube

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