The minimum number of spanning trees in regular multigraphs I: the odd-degree case
J Pekárek, JS Sereni, ZB Yilma - 2021 - hal.science
In a recent article, Bogdanowicz determines the minimum number of spanning trees a
connected cubic multigraph on a fixed number of vertices can have and identifies the unique
graph that attains this minimum value. He conjectures that a generalized form of this
construction, which we here call a padded paddle graph, would be extremal for d-regular
multigraphs where d≥ 5 is odd. We prove that, indeed, the padded paddle minimises the
number of spanning trees, but this is true only when the number of vertices, n, is greater than …
connected cubic multigraph on a fixed number of vertices can have and identifies the unique
graph that attains this minimum value. He conjectures that a generalized form of this
construction, which we here call a padded paddle graph, would be extremal for d-regular
multigraphs where d≥ 5 is odd. We prove that, indeed, the padded paddle minimises the
number of spanning trees, but this is true only when the number of vertices, n, is greater than …
The minimum number of spanning trees in regular multigraphs
J Pekárek, JS Sereni, ZB Yilma - The Electronic Journal of …, 2022 - hal.science
In a recent article, Bogdanowicz determines the minimum number of spanning trees a
connected cubic multigraph on a fixed number of vertices can have and identifies the unique
graph that attains this minimum value. He conjectures that a generalized form of this
construction, which we here call a padded paddle graph, would be extremal for d-regular
multigraphs where d≥ 5 is odd. We prove that, indeed, the padded paddle minimises the
number of spanning trees, but this is true only when the number of vertices, n, is greater than …
connected cubic multigraph on a fixed number of vertices can have and identifies the unique
graph that attains this minimum value. He conjectures that a generalized form of this
construction, which we here call a padded paddle graph, would be extremal for d-regular
multigraphs where d≥ 5 is odd. We prove that, indeed, the padded paddle minimises the
number of spanning trees, but this is true only when the number of vertices, n, is greater than …
以上显示的是最相近的搜索结果。 查看全部搜索结果