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- W4319342972 abstract "Given graphs $T$ and $H$, the generalized Tur'an number ex$(n,T,H)$ is the maximum number of copies of $T$ in an $n$-vertex graph with no copies of $H$. Alon and Shikhelman, using a result of ErdH os, determined the asymptotics of ex$(n,K_3,H)$ when the chromatic number of $H$ is greater than 3 and proved several results when $H$ is bipartite. We consider this problem when $H$ has chromatic number 3. Even this special case for the following relatively simple 3-chromatic graphs appears to be challenging. The suspension $widehat H$ of a graph $H$ is the graph obtained from $H$ by adding a new vertex adjacent to all vertices of $H$. We give new upper and lower bounds on ex$(n,K_3,widehat{H})$ when $H$ is a path, even cycle, or complete bipartite graph. One of the main tools we use is the triangle removal lemma, but it is unclear if much stronger statements can be proved without using the removal lemma." @default.
- W4319342972 created "2023-02-08" @default.
- W4319342972 creator A5036208626 @default.
- W4319342972 creator A5079803922 @default.
- W4319342972 date "2020-04-24" @default.
- W4319342972 modified "2023-09-24" @default.
- W4319342972 title "Triangles in graphs without bipartite suspensions" @default.
- W4319342972 doi "https://doi.org/10.48550/arxiv.2004.11930" @default.
- W4319342972 hasPublicationYear "2020" @default.
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