Matroid invariants and counting graph homomorphisms
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10335152" target="_blank" >RIV/00216208:11320/15:10335152 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.laa.2016.01.022" target="_blank" >http://dx.doi.org/10.1016/j.laa.2016.01.022</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2016.01.022" target="_blank" >10.1016/j.laa.2016.01.022</a>
Alternative languages
Result language
angličtina
Original language name
Matroid invariants and counting graph homomorphisms
Original language description
The number of homomorphisms from a finite graph F to the complete graph K-n is the evaluation of the chromatic polynomial of F at n. Suitably scaled, this is the Tutte polynomial evaluation T(F;1 - n, 0) and an invariant of the cycle matroid of F. De la Harpe and Jaeger [8] asked more generally when is it the case that a graph parameter obtained from counting homomorphisms from F to a fixed graph G depends only on the cycle matroid of F. They showed that this is true when G has a generously transitive automorphism group (examples include Cayley graphs on an abelian group, and Kneser graphs). Using tools from multilinear algebra, we prove the converse statement, thus characterizing finite graphs G for which counting homomorphisms to G yields a matroid invariant. We also extend this result to finite weighted graphs G (where to count homomorphisms from F to G includes such problems as counting nowhere-zero flows of F and evaluating the partition function of an interaction model on F).
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Linear Algebra and Its Applications
ISSN
0024-3795
e-ISSN
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Volume of the periodical
494
Issue of the periodical within the volume
April
Country of publishing house
US - UNITED STATES
Number of pages
11
Pages from-to
263-273
UT code for WoS article
000370891400016
EID of the result in the Scopus database
2-s2.0-84955442741