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On enumeration of spanning trees of complete multipartite graphs containing a fixed spanning forest

Combinatorics 2026-02-04 v1

Abstract

We present a determinantal formula for the number of spanning trees of a complete multipartite graph containing a given spanning forest FF. Our approach relies on the Generalized Matrix Determinant Lemma and Jacobi's formula for the derivative of a determinant. This work generalizes known results for complete bipartite graphs and offers an algebraic perspective on the problem.

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Cite

@article{arxiv.2602.03602,
  title  = {On enumeration of spanning trees of complete multipartite graphs containing a fixed spanning forest},
  author = {Wei Wang and Jun Ge},
  journal= {arXiv preprint arXiv:2602.03602},
  year   = {2026}
}

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11 pages