About: Polynomial graph invariants from homomorphism numbers

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We give a method of generating strongly polynomial sequences of graphs. A classical example is the sequence of complete graphs, for which hom(G,K_k)=P(G;k) is the evaluation of the chromatic polynomial at k. Our construction produces a large family of graph polynomials that 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, related to how many involutive automorphisms with fixed points it has. We prove that a countable family of graphs of bounded branching core size (which in particular implies bounded tree-depth) is always contained in a finite union of strongly polynomial sequences. We give a method of generating strongly polynomial sequences of graphs. A classical example is the sequence of complete graphs, for which hom(G,K_k)=P(G;k) is the evaluation of the chromatic polynomial at k. Our construction produces a large family of graph polynomials that 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, related to how many involutive automorphisms with fixed points it has. We prove that a countable family of graphs of bounded branching core size (which in particular implies bounded tree-depth) is always contained in a finite union of strongly polynomial sequences. (en)
Title	Polynomial graph invariants from homomorphism numbers Polynomial graph invariants from homomorphism numbers (en)
skos:prefLabel	Polynomial graph invariants from homomorphism numbers Polynomial graph invariants from homomorphism numbers (en)
skos:notation	RIV/00216208:11320/13:10173153!RIV14-GA0-11320___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GBP202/12/G061), P(LL1201)
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Nešetřil, Jaroslav Goodall, Andrew
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	97110
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/13:10173153
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	homomorphism numbers; Polynomial graph invariants (en)
http://linked.open.../riv/klicoveSlovo	Polynomial graph invariants homomorphism numbers
http://linked.open...ontrolniKodProRIV	[47F4B61D71CB]
http://linked.open...v/mistoKonaniAkce	Pisa
http://linked.open...i/riv/mistoVydani	Pisa
http://linked.open...i/riv/nazevZdroje	The Seventh European Conference on Combinatorics, Graph Theory and Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Center of excellence - Institute for theoretical computer science (CE-ITI) Complex Structures: Regularities in Combinatorics and Discrete Mathematics
http://linked.open...UplatneniVysledku	2013
http://linked.open...iv/tvurceVysledku	Garijo, Delia Goodall, Andrew Nešetřil, Jaroslav
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2013-09-09 (xsd:date)
number of pages	2 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/978-88-7642-475-5_97
http://purl.org/ne...btex#hasPublisher	Scuola Normale Superiore
https://schema.org/isbn	978-88-7642-474-8
http://localhost/t...ganizacniJednotka	11320

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