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Matching Ensembles (Extended Abstract) [PDF]

Discrete Mathematics & Theoretical Computer Science, 2015
We introduce an axiom system for a collection of matchings that describes the triangulation of product of simplices.
Suho Oh, Hwanchul Yoo
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On the Number of Spanning Trees of New Graph Families Created from the Star Graph and the Examination of Their Entropies

Axioms
Complexity (number of spanning trees) is an essential and significant component in the design of communication networks (graphs). To ensure strong resistance and stiffness and to enhance the probability of a connection between two vertices, improvements ...
Salama Nagy Daoud, Ahmad Asiri
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The Problem of Predecessors on Spanning Trees

Acta Polytechnica, 2011
We consider the equiprobable distribution of spanning trees on the square lattice. All bonds of each tree can be oriented uniquely with respect to an arbitrary chosen site called the root.
V. S. Poghosyan, V. B. Priezzhev
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On the Minimum Number of Spanning Trees in Cubic Multigraphs

Discussiones Mathematicae Graph Theory, 2020
Let G2n, H2n be two non-isomorphic connected cubic multigraphs of order 2n with parallel edges permitted but without loops. Let t(G2n), t (H2n) denote the number of spanning trees in G2n, H2n, respectively. We prove that for n ≥ 3 there is the unique G2n
Bogdanowicz Zbigniew R.
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On the SPANNING k-TREE problem

Discrete Applied Mathematics, 1993
A \(k\)-tree \(T\) is defined recursively as being either a clique of size \(k\) or having a vertex \(x\) whose neighbourhood is a clique of size \(k\) and such that \(T-x\) is a \(k\)-tree. (Note that \(k\)-trees are not trees, if \(k>1\).) The following SPANNING \(k\)-TREE problem is known to be NP-complete: given a graph \(G\), does \(G\) possess a ...
Leizhen Cai, Frédéric Maffray
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The Strong Vertex Span of Trees

Communications on Applied Mathematics and Computation
Abstract The strong vertex (edge) span of a given graph G is the maximum distance that two players can maintain at all times while visiting all vertices (edges) of G and moving either to an adjacent vertex or staying in the current ...
Mateja Grašič, Chris Mouron, Andrej Taranenko   +2 more
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The number of spanning trees of cyclic snakes

Indonesian Journal of Combinatorics
A cyclic snake is a connected graph formed by connecting, by means of vertex amalgamation, a certain number of copies of the cycle Cn, in such a way that the i-th copy of Cn is connected with the (i+1)-th copy, resulting in a graph with maximum degree 4.
Christian Barrientos
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Formulas for the Number of Spanning Trees in a Chain of Cycles

Sultan Qaboos University Journal for Science, 2010
We give a formula for the number of spanning trees in a chain of cycles that have connected intersection of one edge but where the cycles have variable sizes. The formula uses basic properties of continued fractions.
Thomas Bier
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Asymptotic Enumeration of Spanning Trees [PDF]

Combinatorics, Probability and Computing, 2005
We give new formulas for the asymptotics of the number of spanning trees of a large graph. A special case answers a question of McKay [Europ. J. Combin. 4 149–160] for regular graphs. The general answer involves a quantity for infinite graphs that we call ‘tree entropy’, which we show is a logarithm of a normalized determinant of the graph Laplacian ...
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Computing Persistent Homology by Spanning Trees and Critical Simplices. [PDF]

Research (Wash D C), 2023
Shi D, Chen Z, Ma C, Chen G.
europepmc   +1 more source