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A Turán-type theorem for large-distance graphs in Euclidean spaces, and related isodiametric problems
- 1.0508787 - MÚ 2020 RIV SK eng J - Journal Article
Doležal, Martin - Hladký, Jan - Kolář, Jan - Mitsis, T. - Pelekis, Christos - Vlasák, V.
A Turán-type theorem for large-distance graphs in Euclidean spaces, and related isodiametric problems.
Acta Mathematica Universitatis Comenianae. Roč. 88, č. 3 (2019), s. 625-629. ISSN 0231-6986
R&D Projects: GA ČR(CZ) GA17-27844S; GA ČR(CZ) GJ18-01472Y
Institutional support: RVO:67985840
Keywords : large-distance graph * extremal graph theory * Turán's theorem
OECD category: Pure mathematics
Method of publishing: Open access
http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1300
A large-distance graph is a measurable graph whose vertex set is a measurable subset of R^d, and two vertices are connected by an edge if and only if their distance is larger that 2. We address questions from extremal graph theory in the setting of large-distance graphs, focusing in particular on upper-bounds on the measures of vertices and edges of K_r-free large-distance graphs. Our main result states that if Asubset R^2 is a measurable set such that the large-distance graph on $A$ does not contain any complete subgraph on three vertices then the 2-dimensional Lebesgue measure of A is at most 2pi.
Permanent Link: http://hdl.handle.net/11104/0299602
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