Matching polytons

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00512063" target="_blank" >RIV/67985840:_____/19:00512063 - isvavai.cz</a>
Result on the web
<a href="https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i4p38" target="_blank" >https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i4p38</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Matching polytons
Original language description
Hladký, Hu, and Piguet [Tilings in graphons, preprint] introduced the notions of matching and fractional vertex covers in graphons. These are counterparts to the corresponding notions in finite graphs. Combinatorial optimization studies the structure of the matching polytope and the fractional vertex cover polytope of a graph. Here, in analogy, we initiate the study of the structure of the set of all matchings and of all fractional vertex covers in a graphon. We call these sets the matching polyton and the fractional vertex cover polyton. We also study properties of matching polytons and fractional vertex cover polytons along convergent sequences of graphons.As an auxiliary tool of independent interest, we prove that a graphon is r -partite if and only if it contains no graph of chromatic number r+1. This in turn gives a characterization of bipartite graphons as those having a symmetric spectrum.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA16-07378S" target="_blank" >GA16-07378S: Nonlinear analysis in Banach spaces</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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