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- W3174162208 abstract "For a graph G and a family of graphs H, the Turán number ex(G,H) is defined to be the maximum number of edges among all H-free subgraphs of G. Inverting this problem, Briggs and Cox (2019) [5] studied the extremal function εH(k)=sup{e(G)|ex(G,H)<k}, where e(G) is the size of G, and suggested to investigate the extremal function φH(k)=sup{χ(G)|ex(G,H)<k}, where χ(G) denotes the chromatic number of G. Let Kn be a complete graph of order n and H a given graph. In this paper, we establish a tight general upper bound for φH(k) and conjecture φH(k)=max{n|ex(Kn,H)<k} for H≠2K2. We also confirm this conjecture for many instances of H." @default.
- W3174162208 created "2021-07-05" @default.
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- W3174162208 date "2021-09-01" @default.
- W3174162208 modified "2023-10-10" @default.
- W3174162208 title "Inverting the Turán problem with chromatic number" @default.
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- W3174162208 doi "https://doi.org/10.1016/j.disc.2021.112517" @default.
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