Zykov and Erdős showed independently that for $2\le s\le r$, the maximum number of copies of $K_s$ among all $K_r$-free $n$-vertex graphs is achieved uniquely on the complete balanced $r$-partite $n$-vertex graph (Turán graph $T_{n,r}$). When $s=2$, it is the classical theorem of Turán. Nikiforov proved a spectral version of Turán's Theorem. In this paper, we give a spectral version of the theorem by Zykov and Erdős. Our result is a generalization of Nikiforov's Theorem and a theorem of Liu and Bu.
@article{10_37236_14119,
author = {Loujun Yu and Yuejian Peng},
title = {A spectral version of the theorem of {Zykov} and {Erd\H{o}s}},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {4},
doi = {10.37236/14119},
zbl = {8120101},
url = {http://geodesic.mathdoc.fr/articles/10.37236/14119/}
}
TY - JOUR
AU - Loujun Yu
AU - Yuejian Peng
TI - A spectral version of the theorem of Zykov and Erdős
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/14119/
DO - 10.37236/14119
ID - 10_37236_14119
ER -
%0 Journal Article
%A Loujun Yu
%A Yuejian Peng
%T A spectral version of the theorem of Zykov and Erdős
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/14119/
%R 10.37236/14119
%F 10_37236_14119
Loujun Yu; Yuejian Peng. A spectral version of the theorem of Zykov and Erdős. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/14119
