Maximum number of spanning trees and connectivity: Graphs with a fixed minimum degree and bipartite graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912762172538880 |
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| author | Xu, Shaohan Xu, Kexiang Damnjanović, Ivan |
| author_facet | Xu, Shaohan Xu, Kexiang Damnjanović, Ivan |
| contents | The number of spanning trees in a graph $G$ is the total number of distinct spanning subgraphs of $G$ that are trees. In this paper we characterize the unique graph with a prescribed vertex (resp. edge) connectivity, minimum degree and order that attains the maximum number of spanning trees. Moreover, all the bipartite graphs are determined with a given vertex (resp. edge) connectivity and order maximizing the number of spanning trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12308 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximum number of spanning trees and connectivity: Graphs with a fixed minimum degree and bipartite graphs Xu, Shaohan Xu, Kexiang Damnjanović, Ivan Combinatorics 05C05, 05C30, 05C35 The number of spanning trees in a graph $G$ is the total number of distinct spanning subgraphs of $G$ that are trees. In this paper we characterize the unique graph with a prescribed vertex (resp. edge) connectivity, minimum degree and order that attains the maximum number of spanning trees. Moreover, all the bipartite graphs are determined with a given vertex (resp. edge) connectivity and order maximizing the number of spanning trees. |
| title | Maximum number of spanning trees and connectivity: Graphs with a fixed minimum degree and bipartite graphs |
| topic | Combinatorics 05C05, 05C30, 05C35 |
| url | https://arxiv.org/abs/2512.12308 |