par Dujmović, Vida V.;Joret, Gwenaël 
;Micek, Piotr;Morin, Pat P.;Wood, David
Référence Proceedings of the annual ACM-SIAM Symposium on Discrete Algorithms, page (3382-3391)
Publication Publié, 2025-07-01
;Micek, Piotr;Morin, Pat P.;Wood, David Référence Proceedings of the annual ACM-SIAM Symposium on Discrete Algorithms, page (3382-3391)
Publication Publié, 2025-07-01
Article révisé par les pairs
| Résumé : | We show that every n-vertex planar graph is contained in the graph obtained from a fan by blowing up each vertex by a complete graph of order O(√n log2 n). Equivalently, every n-vertex planar graph G has a set X of O(√n log2 n) vertices such that G − X has bandwidth O(√n log2 n). This result holds in the more general setting of graphs contained in the strong product of a bounded treewidth graph and a path, which includes bounded genus graphs, graphs excluding a fixed apex graph as a minor, and k-planar graphs for fixed k. These results are obtained using two ingredients. The first is a new local sparsification lemma, which shows that every n-vertex planar graph G has a set of O((n log n)/D) vertices whose removal results in a graph with local density at most D. The second is a generalization of a method of Feige and Rao, that relates bandwidth and local density using volume-preserving Euclidean embeddings. |
