The Turán number of a graph $H$, $\text{ex}(n,H)$, is the maximum number of edges in an $n$-vertex graph that does not contain $H$ as a subgraph. For a vertex $v$ and a multi-set $\mathcal{F}$ of graphs, the suspension $\mathcal{F}+v$ of $\mathcal{F}$ is the graph obtained by connecting the vertex $v$ to all vertices of $F$ for each $F\in \mathcal{F}$. For two integers $k\ge1$ and $r\ge2$, let $H_i$ be a graph containing a critical edge with chromatic number $r$ for any $i\in\{1,\ldots,k\}$, and let $H=\{H_1,\ldots,H_k\}+v$. In this paper, we determine $\text{ex}(n, H)$ and characterize all the extremal graphs for sufficiently large $n$. This generalizes a result of Chen, Gould, Pfender and Wei on intersecting cliques.
@article{10_37236_12223,
author = {Jianfeng Hou and Heng Li and Qinghou Zeng},
title = {Extremal graphs for the suspension of edge-critical graphs},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {4},
doi = {10.37236/12223},
zbl = {1556.05073},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12223/}
}
TY - JOUR
AU - Jianfeng Hou
AU - Heng Li
AU - Qinghou Zeng
TI - Extremal graphs for the suspension of edge-critical graphs
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/12223/
DO - 10.37236/12223
ID - 10_37236_12223
ER -
%0 Journal Article
%A Jianfeng Hou
%A Heng Li
%A Qinghou Zeng
%T Extremal graphs for the suspension of edge-critical graphs
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/12223/
%R 10.37236/12223
%F 10_37236_12223
Jianfeng Hou; Heng Li; Qinghou Zeng. Extremal graphs for the suspension of edge-critical graphs. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12223
