Polynomial graph invariants from homomorphism numbers

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10333119" target="_blank" >RIV/00216208:11320/16:10333119 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.disc.2015.11.022" target="_blank" >http://dx.doi.org/10.1016/j.disc.2015.11.022</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.disc.2015.11.022" target="_blank" >10.1016/j.disc.2015.11.022</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Polynomial graph invariants from homomorphism numbers

Popis výsledku v původním jazyce

We give a new method of generating strongly polynomial sequences of graphs, i.e., sequences (H-k) indexed by a tuple k = (k(1),..., k(h)) of positive integers, with the property that, for each fixed graph G, there is a multivariate polynomial p(G; x(1),..., x(h)) such that the number of homomorphisms from G to Hk is given by the evaluation p(G; k(1),..., k(h)). A classical example is the sequence of complete graphs (K-k), for which p(G; x) is the chromatic polynomial of G. Our construction is based on tree model representations of graphs. It produces a large family of graph polynomials which includes the Tutte polynomial, the Averbouch Godlin Makowsky polynomial, and the Tittmann Averbouch Makowsky polynomial. We also introduce a new graph parameter, the branching core size of a simple graph, derived from its representation under a particular tree model, and related to how many involutive automorphisms it has. We prove that a countable family of graphs of bounded branching core size is always contained in the union of a finite number of strongly polynomial sequences.

Název v anglickém jazyce

Polynomial graph invariants from homomorphism numbers

Popis výsledku anglicky

We give a new method of generating strongly polynomial sequences of graphs, i.e., sequences (H-k) indexed by a tuple k = (k(1),..., k(h)) of positive integers, with the property that, for each fixed graph G, there is a multivariate polynomial p(G; x(1),..., x(h)) such that the number of homomorphisms from G to Hk is given by the evaluation p(G; k(1),..., k(h)). A classical example is the sequence of complete graphs (K-k), for which p(G; x) is the chromatic polynomial of G. Our construction is based on tree model representations of graphs. It produces a large family of graph polynomials which includes the Tutte polynomial, the Averbouch Godlin Makowsky polynomial, and the Tittmann Averbouch Makowsky polynomial. We also introduce a new graph parameter, the branching core size of a simple graph, derived from its representation under a particular tree model, and related to how many involutive automorphisms it has. We prove that a countable family of graphs of bounded branching core size is always contained in the union of a finite number of strongly polynomial sequences.

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

2016

Kód důvěrnosti údajů

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

Název periodika

Discrete Mathematics

ISSN

0012-365X

e-ISSN

—

Svazek periodika

339

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

1315-1328

Kód UT WoS článku

000369467500015

EID výsledku v databázi Scopus

2-s2.0-84949958321