Matches in SemOpenAlex for { <https://semopenalex.org/work/W4310455004> ?p ?o ?g. }
Showing items 1 to 62 of
62
with 100 items per page.
- W4310455004 abstract "We study the Excluded Grid Theorem, a fundamental structural result in graph theory, that was proved by Robertson and Seymour in their seminal work on graph minors. The theorem states that there is a function $f: mathbb{Z}^+ to mathbb{Z}^+$, such that for every integer $g>0$, every graph of treewidth at least $f(g)$ contains the $(gtimes g)$-grid as a minor. For every integer $g>0$, let $f(g)$ be the smallest value for which the theorem holds. Establishing tight bounds on $f(g)$ is an important graph-theoretic question. Robertson and Seymour showed that $f(g)=Omega(g^2log g)$ must hold. For a long time, the best known upper bounds on $f(g)$ were super-exponential in $g$. The first polynomial upper bound of $f(g)=O(g^{98}text{poly}log g)$ was proved by Chekuri and Chuzhoy. It was later improved to $f(g) = O(g^{36}text{poly} log g)$, and then to $f(g)=O(g^{19}text{poly}log g)$. In this paper we further improve this bound to $f(g)=O(g^{9}text{poly} log g)$. We believe that our proof is significantly simpler than the proofs of the previous bounds. Moreover, while there are natural barriers that seem to prevent the previous methods from yielding tight bounds for the theorem, it seems conceivable that the techniques proposed in this paper can lead to even tighter bounds on $f(g)$." @default.
- W4310455004 created "2022-12-10" @default.
- W4310455004 creator A5056023203 @default.
- W4310455004 creator A5072885035 @default.
- W4310455004 date "2019-01-23" @default.
- W4310455004 modified "2023-09-27" @default.
- W4310455004 title "Towards Tight(er) Bounds for the Excluded Grid Theorem" @default.
- W4310455004 doi "https://doi.org/10.48550/arxiv.1901.07944" @default.
- W4310455004 hasPublicationYear "2019" @default.
- W4310455004 type Work @default.
- W4310455004 citedByCount "0" @default.
- W4310455004 crossrefType "posted-content" @default.
- W4310455004 hasAuthorship W4310455004A5056023203 @default.
- W4310455004 hasAuthorship W4310455004A5072885035 @default.
- W4310455004 hasBestOaLocation W43104550041 @default.
- W4310455004 hasConcept C114614502 @default.
- W4310455004 hasConcept C118615104 @default.
- W4310455004 hasConcept C121332964 @default.
- W4310455004 hasConcept C132525143 @default.
- W4310455004 hasConcept C132569581 @default.
- W4310455004 hasConcept C134306372 @default.
- W4310455004 hasConcept C199360897 @default.
- W4310455004 hasConcept C203776342 @default.
- W4310455004 hasConcept C2779557605 @default.
- W4310455004 hasConcept C33923547 @default.
- W4310455004 hasConcept C41008148 @default.
- W4310455004 hasConcept C43517604 @default.
- W4310455004 hasConcept C62520636 @default.
- W4310455004 hasConcept C77553402 @default.
- W4310455004 hasConcept C97137487 @default.
- W4310455004 hasConceptScore W4310455004C114614502 @default.
- W4310455004 hasConceptScore W4310455004C118615104 @default.
- W4310455004 hasConceptScore W4310455004C121332964 @default.
- W4310455004 hasConceptScore W4310455004C132525143 @default.
- W4310455004 hasConceptScore W4310455004C132569581 @default.
- W4310455004 hasConceptScore W4310455004C134306372 @default.
- W4310455004 hasConceptScore W4310455004C199360897 @default.
- W4310455004 hasConceptScore W4310455004C203776342 @default.
- W4310455004 hasConceptScore W4310455004C2779557605 @default.
- W4310455004 hasConceptScore W4310455004C33923547 @default.
- W4310455004 hasConceptScore W4310455004C41008148 @default.
- W4310455004 hasConceptScore W4310455004C43517604 @default.
- W4310455004 hasConceptScore W4310455004C62520636 @default.
- W4310455004 hasConceptScore W4310455004C77553402 @default.
- W4310455004 hasConceptScore W4310455004C97137487 @default.
- W4310455004 hasLocation W43104550041 @default.
- W4310455004 hasLocation W43104550042 @default.
- W4310455004 hasOpenAccess W4310455004 @default.
- W4310455004 hasPrimaryLocation W43104550041 @default.
- W4310455004 hasRelatedWork W1985880617 @default.
- W4310455004 hasRelatedWork W2178269805 @default.
- W4310455004 hasRelatedWork W2393028428 @default.
- W4310455004 hasRelatedWork W3134208201 @default.
- W4310455004 hasRelatedWork W4225370530 @default.
- W4310455004 hasRelatedWork W4296603869 @default.
- W4310455004 hasRelatedWork W4321393130 @default.
- W4310455004 hasRelatedWork W4377372033 @default.
- W4310455004 hasRelatedWork W4384339936 @default.
- W4310455004 hasRelatedWork W4386721782 @default.
- W4310455004 isParatext "false" @default.
- W4310455004 isRetracted "false" @default.
- W4310455004 workType "article" @default.