Counting Isomorphism Classes of Spanning Trees of Complete Bipartite Graphs
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918365588619264 |
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| author | Johnson, Peter Nochumson, Shayne |
| author_facet | Johnson, Peter Nochumson, Shayne |
| contents | Spanning trees of complete bipartite graphs exhibit a rich interaction between degree sequences and graph structure. In this paper, we obtain lower bounds on the number of isomorphism classes of spanning trees in $K_{a,b}, 2 \leq a \leq b$ in terms of $P_a(a+b-1)$ and $P_b(a+b-1)$ where $P_k(m)$ is the number of integer partitions of $m$ of length $k$. Furthermore, we obtain an upper bound in terms of $a$ and $b$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06867 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Counting Isomorphism Classes of Spanning Trees of Complete Bipartite Graphs Johnson, Peter Nochumson, Shayne Combinatorics 05C40, 05C60, 05C75 Spanning trees of complete bipartite graphs exhibit a rich interaction between degree sequences and graph structure. In this paper, we obtain lower bounds on the number of isomorphism classes of spanning trees in $K_{a,b}, 2 \leq a \leq b$ in terms of $P_a(a+b-1)$ and $P_b(a+b-1)$ where $P_k(m)$ is the number of integer partitions of $m$ of length $k$. Furthermore, we obtain an upper bound in terms of $a$ and $b$. |
| title | Counting Isomorphism Classes of Spanning Trees of Complete Bipartite Graphs |
| topic | Combinatorics 05C40, 05C60, 05C75 |
| url | https://arxiv.org/abs/2602.06867 |