Matroid invariants and counting graph homomorphisms

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Matroid invariants and counting graph homomorphisms

Popis výsledku v původním jazyce

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).

Název v anglickém jazyce

Matroid invariants and counting graph homomorphisms

Popis výsledku anglicky

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).

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Linear Algebra and Its Applications

ISSN

0024-3795

e-ISSN

—

Svazek periodika

494

Číslo periodika v rámci svazku

April

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

11

Strana od-do

263-273

Kód UT WoS článku

000370891400016

EID výsledku v databázi Scopus

2-s2.0-84955442741