Polynomial graph invariants from homomorphism numbers

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Polynomial graph invariants from homomorphism numbers
Original language description
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.
Czech name
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Czech description
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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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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)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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