PreprintarXiv licencearXiv
The minimum number of wheel-saturating edges
Abstract
Let G be an H-free graph and e be a non-edge of G. We say e is an H-saturating edge of G, if G+e contains a copy of H. We denote by fH(n,m) the minimum number of H-saturating edges of an n-vertex H-free graph with exactly m edges. In this paper, we show that fW2k+1(n,ex(n,F2k+1)+1)= ℓ −k, &(k−2)ℓ is even, 2(ℓ−k)−1, &(k−2)ℓ is odd, and fW2k(n,ex(n,F2k)+1)=(2/33+o(1))n2. At the same time, we characterize the corresponding extremal graphs.
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BibTeX
@misc{chen2026minimum,
title = {{The minimum number of wheel-saturating edges}},
author = {Xianglei Chen and Changxiang He},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33041},
eprint = {2610.33041},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33041},
}
RIS
TY - UNPB
TI - The minimum number of wheel-saturating edges
AU - Xianglei Chen
AU - Changxiang He
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.33041
UR - https://arxiv.org/abs/2610.33041
AB - Let G be an H-free graph and e be a non-edge of G. We say e is an H-saturating edge of G, if G+e contains a copy of H. We denote by f_H(n,m) the minimum number of H-saturating edges of an n-vertex H-free graph with exactly m edges. In this paper, we show that f_W_2k+1(n,ex(n,F_2k+1)+1)= ℓ −k, &(k−2)ℓ is even, 2(ℓ−k)−1, &(k−2)ℓ is odd, and f_W_2k(n,ex(n,F_2k)+1)=(2/33+o(1))n^2. At the same time, we characterize the corresponding extremal graphs.
ER -