The canonical Tutte polynomial for signed graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10404768" target="_blank" >RIV/00216208:11320/19:10404768 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=jGfJCQXusX" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=jGfJCQXusX</a>

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

The canonical Tutte polynomial for signed graphs

Popis výsledku v původním jazyce

We construct a new polynomial invariant for signed graphs, the trivariate Tutte polynomial, which contains among its evaluations the number of proper colorings and the number of nowhere-zero flows. In this, it parallels the Tutte polynomial of a graph, which contains the chromatic polynomial and flow polynomial as specializations. While the Tutte polynomial of a graph is equivalently defined as the dichromatic polynomial or Whitney rank polynomial, the dichromatic polynomial of a signed graph (defined more widely for biased graphs by Zaslavsky) does not, by contrast, give the number of nowhere-zero flows as an evaluation in general. The trivariate Tutte polynomial contains Zaslavsky&apos;s dichromatic polynomial as a specialization. Furthermore, the trivariate Tutte polynomial gives as an evaluation the number of proper colorings of a signed graph under a more general sense of signed graph coloring in which colors are elements of an arbitrary finite set equipped with an involution.

Název v anglickém jazyce

The canonical Tutte polynomial for signed graphs

Popis výsledku anglicky

We construct a new polynomial invariant for signed graphs, the trivariate Tutte polynomial, which contains among its evaluations the number of proper colorings and the number of nowhere-zero flows. In this, it parallels the Tutte polynomial of a graph, which contains the chromatic polynomial and flow polynomial as specializations. While the Tutte polynomial of a graph is equivalently defined as the dichromatic polynomial or Whitney rank polynomial, the dichromatic polynomial of a signed graph (defined more widely for biased graphs by Zaslavsky) does not, by contrast, give the number of nowhere-zero flows as an evaluation in general. The trivariate Tutte polynomial contains Zaslavsky&apos;s dichromatic polynomial as a specialization. Furthermore, the trivariate Tutte polynomial gives as an evaluation the number of proper colorings of a signed graph under a more general sense of signed graph coloring in which colors are elements of an arbitrary finite set equipped with an involution.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA19-21082S" target="_blank" >GA19-21082S: Grafy a jejich algebraické vlastnosti</a><br>

Návaznosti

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

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Acta Mathematica Universitatis Comenianae

ISSN

0231-6986

e-ISSN

—

Svazek periodika

88

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

SK - Slovenská republika

Počet stran výsledku

6

Strana od-do

749-754

Kód UT WoS článku

000484349000061

EID výsledku v databázi Scopus

—