Author:
Győri Ervin,He Zhen,Lv Zequn,Salia Nika,Tompkins Casey,Zhu Xiutao
Abstract
We resolve a conjecture of Cox and Martin by determining asymptotically for every $k\ge 2$ the maximum number of copies of $C_{2k}$ in an $n$-vertex planar graph.
Reference11 articles.
1. Noga Alon and Yair Caro. On the number of subgraphs of prescribed type of pla- nar graphs with a given number of vertices. In North-Holland Mathematics Studies, volume 87, pages 25-36. Elsevier, 1984.
2. Asaf Cohen Antonir and Asaf Shapira. Bounding the number of odd paths in planar graphs via convex optimization. arXiv preprint arXiv:2208.02097, 2022.
3. Christopher Cox and Ryan R Martin. Counting paths, cycles, and blow-ups in planar graphs. Journal of Graph Theory, 101(3):521-558, 2022.
4. Christopher Cox and Ryan R Martin. The maximum number of 10-and 12-cycles in a planar graph. Discrete Mathematics, 346(2):113245, 2023.
5. David Eppstein. Connectivity, graph minors, and subgraph multiplicity. Journal of Graph Theory, 17(3):409-416, 1993.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献