Matches in SemOpenAlex for { <https://semopenalex.org/work/W4300302595> ?p ?o ?g. }
Showing items 1 to 41 of
41
with 100 items per page.
- W4300302595 abstract "For a field $F$ and a quadratic form $Q$ defined on an $n$-dimensional vector space $V$ over $F$, let $mathrm{QG}_Q$, called the quadratic graph associated to $Q$, be the graph with the vertex set $V$ where vertices $u,w in V$ form an edge if and only if $Q(v-w)=1$. Quadratic graphs can be viewed as natural generalizations of the unit-distance graph featuring in the famous Hadwiger-Nelson problem. In the present paper, we will prove that for a local field $F$ of characteristic zero, the Borel chromatic number of $mathrm{QG}_Q$ is infinite if and only if $Q$ represents zero non-trivially over $F$. The proof employs a recent spectral bound for the Borel chromatic number of Cayley graphs, combined with an analysis of certain oscillatory integrals over local fields. As an application, we will also answer a variant of question 525 proposed in the 22nd British Combinatorics Conference 2009." @default.
- W4300302595 created "2022-10-03" @default.
- W4300302595 creator A5045654028 @default.
- W4300302595 creator A5089032259 @default.
- W4300302595 date "2015-07-19" @default.
- W4300302595 modified "2023-09-27" @default.
- W4300302595 title "On a generalization of the Hadwiger-Nelson problem" @default.
- W4300302595 doi "https://doi.org/10.48550/arxiv.1507.05300" @default.
- W4300302595 hasPublicationYear "2015" @default.
- W4300302595 type Work @default.
- W4300302595 citedByCount "0" @default.
- W4300302595 crossrefType "posted-content" @default.
- W4300302595 hasAuthorship W4300302595A5045654028 @default.
- W4300302595 hasAuthorship W4300302595A5089032259 @default.
- W4300302595 hasBestOaLocation W43003025951 @default.
- W4300302595 hasConcept C114614502 @default.
- W4300302595 hasConcept C118615104 @default.
- W4300302595 hasConcept C132525143 @default.
- W4300302595 hasConcept C33923547 @default.
- W4300302595 hasConcept C80899671 @default.
- W4300302595 hasConceptScore W4300302595C114614502 @default.
- W4300302595 hasConceptScore W4300302595C118615104 @default.
- W4300302595 hasConceptScore W4300302595C132525143 @default.
- W4300302595 hasConceptScore W4300302595C33923547 @default.
- W4300302595 hasConceptScore W4300302595C80899671 @default.
- W4300302595 hasLocation W43003025951 @default.
- W4300302595 hasOpenAccess W4300302595 @default.
- W4300302595 hasPrimaryLocation W43003025951 @default.
- W4300302595 hasRelatedWork W1719252778 @default.
- W4300302595 hasRelatedWork W2008276241 @default.
- W4300302595 hasRelatedWork W2031098440 @default.
- W4300302595 hasRelatedWork W2034217845 @default.
- W4300302595 hasRelatedWork W2169820283 @default.
- W4300302595 hasRelatedWork W2374778222 @default.
- W4300302595 hasRelatedWork W2555545330 @default.
- W4300302595 hasRelatedWork W2964041938 @default.
- W4300302595 hasRelatedWork W4307385446 @default.
- W4300302595 hasRelatedWork W922283457 @default.
- W4300302595 isParatext "false" @default.
- W4300302595 isRetracted "false" @default.
- W4300302595 workType "article" @default.