LARGE -FREE SUBGRAPHS IN -CHROMATIC GRAPHS

Abstract For a graph G and a family of graphs $\mathcal {F}$ , the Turán number ${\mathrm {ex}}(G,\mathcal {F})$ is the maximum number of edges an $\mathcal {F}$ -free subgraph of G can have. We prove that ${\mathrm {ex}}(G,\mathcal {F})\ge {\mathrm {ex}}(K_r, \mathcal {F})$ if the chromatic number...

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 2023-10, Vol.108 (2), p.200-204
Main Authors: HE, ZHEN, LV, ZEQUN, ZHU, XIUTAO
Format: Article
Language:English
Subjects:
Graph theory
Graphs
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Summary:Abstract For a graph G and a family of graphs $\mathcal {F}$ , the Turán number ${\mathrm {ex}}(G,\mathcal {F})$ is the maximum number of edges an $\mathcal {F}$ -free subgraph of G can have. We prove that ${\mathrm {ex}}(G,\mathcal {F})\ge {\mathrm {ex}}(K_r, \mathcal {F})$ if the chromatic number of G is r and $\mathcal {F}$ is a family of connected graphs. This result answers a question raised by Briggs and Cox [‘Inverting the Turán problem’, Discrete Math. 342 (7) (2019), 1865–1884] about the inverse Turán number for all connected graphs.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972722001319