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pro vyhledávání: '"Klee, Steven"'
We prove the following sharp estimate for the number of spanning trees of a graph in terms of its vertex-degrees: a simple graph $G$ on $n$ vertices has at most $(1/n^{2}) \prod_{v \in V(G)} (d(v)+1)$ spanning trees. This result is tight (for complet
Externí odkaz:
http://arxiv.org/abs/2102.01669
Autor:
Klee, Steven, Stamps, Matthew T.
We show how the spectrum of a graph Laplacian changes with respect to a certain type of rank-one perturbation. We apply our finding to give new short proofs of the spectral version of Kirchhoff's Matrix Tree Theorem and known derivations for the char
Externí odkaz:
http://arxiv.org/abs/2008.01669
Oriented matroids (often called order types) are combinatorial structures that generalize point configurations, vector configurations, hyperplane arrangements, polyhedra, linear programs, and directed graphs. Oriented matroids have played a key role
Externí odkaz:
http://arxiv.org/abs/2006.08922
Autor:
Klee, Steven, Stamps, Matthew T.
Publikováno v:
The American Mathematical Monthly, 127:4, 297-307 (2020)
Kirchhoff's Matrix-Tree Theorem asserts that the number of spanning trees in a finite graph can be computed from the determinant of any of its reduced Laplacian matrices. In many cases, even for well-studied families of graphs, this can be computatio
Externí odkaz:
http://arxiv.org/abs/1903.04973
Autor:
Klee, Steven, Stamps, Matthew T.
Publikováno v:
Linear Algebra and its Applications, Volume 582, 2019, Pages 391-402
The weighted spanning tree enumerator of a graph $G$ with weighted edges is the sum of the products of edge weights over all the spanning trees in $G$. In the special case that all of the edge weights equal $1$, the weighted spanning tree enumerator
Externí odkaz:
http://arxiv.org/abs/1903.03575
Autor:
Klee, Steven, Nugent, Brian
We show that the $h$-vector of a $2$-dimensional PS ear-decomposable simplicial complex is a pure $\mathcal{O}$-sequence. This provides a strengthening of Stanley's conjecture for matroid $h$-vectors in rank $3$. Our approach modifies the approach of
Externí odkaz:
http://arxiv.org/abs/1811.04059
Stanley proved that for any centrally symmetric simplicial $d$-polytope $P$ with $d\geq 3$, $g_2(P) \geq {d \choose 2}-d$. We provide a characterization of centrally symmetric $d$-polytopes with $d\geq 4$ that satisfy this inequality as equality. Thi
Externí odkaz:
http://arxiv.org/abs/1706.03447
Autor:
Klee, Steven, Stamps, Matthew T.
Publikováno v:
The American Mathematical Monthly, 2020 Apr 01. 127(4), 297-307.
Externí odkaz:
https://www.jstor.org/stable/48662205
We introduce a notion of cross-flips: local moves that transform a balanced (i.e., properly $(d+1)$-colored) triangulation of a combinatorial $d$-manifold into another balanced triangulation. These moves form a natural analog of bistellar flips (also
Externí odkaz:
http://arxiv.org/abs/1512.04384