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Pré-Publication, Document De Travail Année : 2023

The number of spanning trees in 4-regular simple graphs

Le nombre d'arbres couvrants des graphes simples 4-réguliers

Zelealem B Yilma
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Résumé

Extending an earlier work by Kostochka for subcubic graphs, we show that a connected graph G with minimum degree 2 and maximum degree 4 has at least 75^(1/10·(2·n_4 + n_3 + 2)) spanning trees, where n_i is the number of vertices of degree i in G, unless G is the complete graph on 5 vertices or obtained from the complete graph on 6 vertices by deleting the edges of a perfect matching. This, in particular, allows us to determine the value of the inferior limit of the normalised number of spanning trees (introduced by Alon) over the class of connected 4-regular graphs to be 75^(1/5 ).
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Dates et versions

hal-04301905 , version 1 (23-11-2023)

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  • HAL Id : hal-04301905 , version 1

Citer

Jean-Sébastien Sereni, Zelealem B Yilma. The number of spanning trees in 4-regular simple graphs. 2023. ⟨hal-04301905⟩

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