An Improved Planar Graph Product Structure Theorem
نویسندگان
چکیده
Dujmović, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every planar graph $G$ there is a $H$ with treewidth at most 8 path $P$ such $G\subseteq H\boxtimes P$. We improve this result by replacing "treewidth 8" "simple 6".
منابع مشابه
Unprovability threshold for planar graph minor theorem
This note is part of implementation of a programme in foundations of mathematics to find exact threshold versions of all mathematical unprovability results known so far, a programme initiated by A. Weiermann. Here we find the exact versions of unprovability of the finite graph minor theorem restricted to planar graphs, connected planar graphs and graphs embeddable into a given surface, assuming...
متن کاملUnprovability threshold for the planar graph minor theorem
This note is part of implementation of a programme in foundations of mathematics to find exact threshold versions of all mathematical unprovability results known so far, a programme initiated by A. Weiermann. Here we find the exact versions of unprovability of the finite graph minor theorem with growth rate condition restricted to planar graphs, connected planar graphs and graphs embeddable int...
متن کاملOptimizing the Graph Minors Weak Structure Theorem
Abstract. One of the major results of [N. Robertson and P. D. Seymour. Graph minors. XIII. The disjoint paths problem. J. Combin. Theory Ser. B, 63(1):65–110, 1995], also known as the weak structure theorem, reveals the local structure of graphs excluding some graph as a minor: each such graph G either has small treewidth or contains the subdivision of a planar graph (a wall) that can be arrang...
متن کاملComplete graph minors and the graph minor structure theorem
Article history: Received 19 May 2011 Available online xxxx
متن کاملAn Improved Randomized Data Structure for Dynamic Graph Connectivity
We present a randomized algorithm for dynamic graph connectivity. With failure probability less than 1/n (for any constant c we choose), our solution has worst case running time O(log n) per edge insertion, O(log n) per edge deletion, and O(log n/ log log n) per query, where n is the number of vertices. The previous best algorithm has worst case running time O(log n) per edge insertion and O(lo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Journal of Combinatorics
سال: 2022
ISSN: ['1077-8926', '1097-1440']
DOI: https://doi.org/10.37236/10614