Common graphs with arbitrary connectivity and chromatic number
- Authors
- Ko, Sejin; Lee, Joonkyung
- Issue Date
- Sep-2023
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Ramsey multiplicity; Common graphs; Graph homomorphism inequalities; (Hyper)graph connectivity
- Citation
- JOURNAL OF COMBINATORIAL THEORY SERIES B, v.162, pp 223 - 230
- Pages
- 8
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF COMBINATORIAL THEORY SERIES B
- Volume
- 162
- Start Page
- 223
- End Page
- 230
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/189397
- DOI
- 10.1016/j.jctb.2023.06.001
- ISSN
- 0095-8956
1096-0902
- Abstract
- A graph H is common if the number of monochromatic copies of H in a 2-edge-colouring of the complete graph Kn is asymptotically minimised by the random colouring. We prove that, given k,r>0, there exists a k-connected common graph with chromatic number at least r. The result is built upon the recent breakthrough of Kráľ, Volec, and Wei who obtained common graphs with arbitrarily large chromatic number and answers a question of theirs.
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