Let $C_k$ be a cycle of order $k$, where $k\ge 3$. Let ex$(n, n, n, \{C_{3}, C_{4}\})$ be the maximum number of edges in a balanced $3$-partite graph whose vertex set consists of three parts, each has $n$ vertices that has no subgraph isomorphic to $C_3$ or $C_4$. We construct dense balanced 3-partite graphs without 3-cycles or 4-cycles and show that ex$(n, n, n, \{C_{3}, C_{4}\})\ge (\frac{6\sqrt{2}-8}{(\sqrt{2}-1)^{3/2}}+o(1))n^{3/2}$.
@article{10_37236_10958,
author = {Zequn Lv and Mei Lu and Chunqiu Fang},
title = {Density of balanced 3-partite graphs without 3-cycles or 4-cycles},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {4},
doi = {10.37236/10958},
zbl = {1506.05075},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10958/}
}
TY - JOUR
AU - Zequn Lv
AU - Mei Lu
AU - Chunqiu Fang
TI - Density of balanced 3-partite graphs without 3-cycles or 4-cycles
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/10958/
DO - 10.37236/10958
ID - 10_37236_10958
ER -
%0 Journal Article
%A Zequn Lv
%A Mei Lu
%A Chunqiu Fang
%T Density of balanced 3-partite graphs without 3-cycles or 4-cycles
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/10958/
%R 10.37236/10958
%F 10_37236_10958
Zequn Lv; Mei Lu; Chunqiu Fang. Density of balanced 3-partite graphs without 3-cycles or 4-cycles. The electronic journal of combinatorics, Tome 29 (2022) no. 4. doi: 10.37236/10958
