Counting unbranched subgraphs
type: Item
instance of: scholarly article
title: Counting unbranched subgraphs
zbMATH Open document ID: 0915.05068
DOI: 10.1023/A:1018690328814
published in: Journal of Algebraic Combinatorics
publication date: 1999-06-23T00:00:00Z
review text: For a given graph \(G=(V,E)\), its unbranched subgraph is defined to be an edge-induced spanning subgraph such that the degree of each vertex is not greater than 2. The main result shows that the real part of any root of the polynomial \[ Q(z)=\sum_{F}z^{| F| }, \] where \(F\) is taken over all the subsets of \(E\) such that \(F\) forms an unbranched subgraph of \(G\), is always negative.
Mathematics Subject Classification ID: 05C30
zbMATH DE Number: 1275697
zbMATH Keywords: unbranched subgraph
zbMATH Keywords: counting polynomial
author: David Ruelle
reviewed by: Yanpei Liu
MaRDI profile type: Publication
cites work: Theorems on the Partition Functions of the Heisenberg Ferromagnets
cites work: Theory of monomer-dimer systems
cites work: Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model
cites work: Multipartition Series
description: scientific article; zbMATH DE number 1275697