Matching polytons

0512063 - MÚ 2020 RIV US eng J - Journal Article
Doležal, Martin - Hladký, Jan
Matching polytons.
Electronic Journal of Combinatorics. Roč. 26, č. 4 (2019), č. článku P4.38. ISSN 1077-8926. E-ISSN 1077-8926
R&D Projects: GA ČR GA16-07378S
EU Projects: European Commission(XE) 628974 - PAECIDM
Institutional support: RVO:67985840
Keywords : graphon * matching polytope
OECD category: Pure mathematics
Impact factor: 0.641, year: 2019
Method of publishing: Open access
https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i4p38

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.
Permanent Link: http://hdl.handle.net/11104/0302266