Let $k\ge 2$ and $n_1\ge n_2\ge n_3\ge n_4$ be integers such that $n_4$ is sufficiently larger than $k$. We determine the maximum number of edges of a 4-partite graph with parts of sizes $n_1,\dots, n_4$ that does not contain $k$ vertex-disjoint triangles. For any $r> t\ge 3$, we give a conjecture on the maximum number of edges of an $r$-partite graph that does not contain $k$ vertex-disjoint cliques $K_t$.
@article{10_37236_10148,
author = {Jie Han and Yi Zhao},
title = {Tur\'an number of disjoint triangles in 4-partite graphs},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {2},
doi = {10.37236/10148},
zbl = {1491.05104},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10148/}
}
TY - JOUR
AU - Jie Han
AU - Yi Zhao
TI - Turán number of disjoint triangles in 4-partite graphs
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/10148/
DO - 10.37236/10148
ID - 10_37236_10148
ER -
%0 Journal Article
%A Jie Han
%A Yi Zhao
%T Turán number of disjoint triangles in 4-partite graphs
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/10148/
%R 10.37236/10148
%F 10_37236_10148
Jie Han; Yi Zhao. Turán number of disjoint triangles in 4-partite graphs. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/10148
