Non-Bipartite K-Common Graphs

Daniel Král’; Jonathan A. Noel; Sergey Norin; Jan Volec; Fan Wei

doi:10.1007/s00493-020-4499-9

Non-Bipartite K-Common Graphs

Daniel Král’, Jonathan A. Noel, Sergey Norin, Jan Volec, Fan Wei

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of K_n is asymptotically minimized by a random coloring. For every k, we construct a connected non-bipartite k-common graph. This resolves a problem raised by Jagger, Štovíček and Thomason [20]. We also show that a graph H is k-common for every k if and only if H is Sidorenko and that H is locally k-common for every k if and only if H is locally Sidorenko.

Original language	English (US)
Pages (from-to)	87-114
Number of pages	28
Journal	Combinatorica
Volume	42
Issue number	1
DOIs	https://doi.org/10.1007/s00493-020-4499-9
State	Published - Feb 2022

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1007/s00493-020-4499-9

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title = "Non-Bipartite K-Common Graphs",

abstract = "A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of Kn is asymptotically minimized by a random coloring. For every k, we construct a connected non-bipartite k-common graph. This resolves a problem raised by Jagger, {\v S}tov{\'i}{\v c}ek and Thomason [20]. We also show that a graph H is k-common for every k if and only if H is Sidorenko and that H is locally k-common for every k if and only if H is locally Sidorenko.",

author = "Daniel Kr{\'a}l{\textquoteright} and Noel, \{Jonathan A.\} and Sergey Norin and Jan Volec and Fan Wei",

note = "Publisher Copyright: {\textcopyright} 2022, J{\'a}nos Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg.",

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doi = "10.1007/s00493-020-4499-9",

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T1 - Non-Bipartite K-Common Graphs

AU - Král’, Daniel

AU - Noel, Jonathan A.

AU - Norin, Sergey

AU - Volec, Jan

AU - Wei, Fan

PY - 2022/2

Y1 - 2022/2

N2 - A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of Kn is asymptotically minimized by a random coloring. For every k, we construct a connected non-bipartite k-common graph. This resolves a problem raised by Jagger, Štovíček and Thomason [20]. We also show that a graph H is k-common for every k if and only if H is Sidorenko and that H is locally k-common for every k if and only if H is locally Sidorenko.

AB - A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of Kn is asymptotically minimized by a random coloring. For every k, we construct a connected non-bipartite k-common graph. This resolves a problem raised by Jagger, Štovíček and Thomason [20]. We also show that a graph H is k-common for every k if and only if H is Sidorenko and that H is locally k-common for every k if and only if H is locally Sidorenko.

UR - https://www.scopus.com/pages/publications/85124762881

UR - https://www.scopus.com/inward/citedby.url?scp=85124762881&partnerID=8YFLogxK

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DO - 10.1007/s00493-020-4499-9

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SP - 87

EP - 114

JO - Combinatorica

JF - Combinatorica

IS - 1

ER -

Non-Bipartite K-Common Graphs

Abstract

All Science Journal Classification (ASJC) codes

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