Matches in SemOpenAlex for { <https://semopenalex.org/work/W4287993535> ?p ?o ?g. }
Showing items 1 to 68 of
68
with 100 items per page.
- W4287993535 abstract "If we want to color $1,2,ldots,n$ with the property that all 3-term arithmetic progressions are rainbow (that is, their elements receive 3 distinct colors), then, obviously, we need to use at least $n/2$ colors. Surprisingly, much fewer colors suffice if we are allowed to leave a negligible proportion of integers uncolored. Specifically, we prove that there exist $alpha,beta<1$ such that for every $n$, there is a subset $A$ of ${1,2,ldots,n}$ of size at least $n-n^{alpha}$, the elements of which can be colored with $n^{beta}$ colors with the property that every 3-term arithmetic progression in $A$ is rainbow. Moreover, $beta$ can be chosen to be arbitrarily small. Our result can be easily extended to $k$-term arithmetic progressions for any $kge 3$. As a corollary, we obtain the following result of Alon, Moitra, and Sudakov, which can be used to design efficient communication protocols over shared directional multi-channels. There exist $alpha',beta'<1$ such that for every $n$, there is a graph with $n$ vertices and at least $binom{n}{2}-n^{1+alpha'}$ edges, whose edge set can be partitioned into at most $n^{1+beta'}$ induced matchings." @default.
- W4287993535 created "2022-07-26" @default.
- W4287993535 creator A5032398271 @default.
- W4287993535 creator A5040332950 @default.
- W4287993535 date "2019-12-16" @default.
- W4287993535 modified "2023-10-06" @default.
- W4287993535 title "Colorings with only rainbow arithmetic progressions" @default.
- W4287993535 doi "https://doi.org/10.48550/arxiv.1912.07470" @default.
- W4287993535 hasPublicationYear "2019" @default.
- W4287993535 type Work @default.
- W4287993535 citedByCount "0" @default.
- W4287993535 crossrefType "posted-content" @default.
- W4287993535 hasAuthorship W4287993535A5032398271 @default.
- W4287993535 hasAuthorship W4287993535A5040332950 @default.
- W4287993535 hasBestOaLocation W42879935351 @default.
- W4287993535 hasConcept C105795698 @default.
- W4287993535 hasConcept C114614502 @default.
- W4287993535 hasConcept C118615104 @default.
- W4287993535 hasConcept C121332964 @default.
- W4287993535 hasConcept C130498168 @default.
- W4287993535 hasConcept C132525143 @default.
- W4287993535 hasConcept C159985019 @default.
- W4287993535 hasConcept C171606756 @default.
- W4287993535 hasConcept C192562407 @default.
- W4287993535 hasConcept C2776558979 @default.
- W4287993535 hasConcept C2778307483 @default.
- W4287993535 hasConcept C2780012671 @default.
- W4287993535 hasConcept C33923547 @default.
- W4287993535 hasConcept C49453240 @default.
- W4287993535 hasConcept C61797465 @default.
- W4287993535 hasConcept C62520636 @default.
- W4287993535 hasConcept C64943373 @default.
- W4287993535 hasConcept C94375191 @default.
- W4287993535 hasConceptScore W4287993535C105795698 @default.
- W4287993535 hasConceptScore W4287993535C114614502 @default.
- W4287993535 hasConceptScore W4287993535C118615104 @default.
- W4287993535 hasConceptScore W4287993535C121332964 @default.
- W4287993535 hasConceptScore W4287993535C130498168 @default.
- W4287993535 hasConceptScore W4287993535C132525143 @default.
- W4287993535 hasConceptScore W4287993535C159985019 @default.
- W4287993535 hasConceptScore W4287993535C171606756 @default.
- W4287993535 hasConceptScore W4287993535C192562407 @default.
- W4287993535 hasConceptScore W4287993535C2776558979 @default.
- W4287993535 hasConceptScore W4287993535C2778307483 @default.
- W4287993535 hasConceptScore W4287993535C2780012671 @default.
- W4287993535 hasConceptScore W4287993535C33923547 @default.
- W4287993535 hasConceptScore W4287993535C49453240 @default.
- W4287993535 hasConceptScore W4287993535C61797465 @default.
- W4287993535 hasConceptScore W4287993535C62520636 @default.
- W4287993535 hasConceptScore W4287993535C64943373 @default.
- W4287993535 hasConceptScore W4287993535C94375191 @default.
- W4287993535 hasLocation W42879935351 @default.
- W4287993535 hasLocation W42879935352 @default.
- W4287993535 hasOpenAccess W4287993535 @default.
- W4287993535 hasPrimaryLocation W42879935351 @default.
- W4287993535 hasRelatedWork W1880776363 @default.
- W4287993535 hasRelatedWork W2171590215 @default.
- W4287993535 hasRelatedWork W2396902672 @default.
- W4287993535 hasRelatedWork W2884900153 @default.
- W4287993535 hasRelatedWork W2897079380 @default.
- W4287993535 hasRelatedWork W2979686890 @default.
- W4287993535 hasRelatedWork W2980821823 @default.
- W4287993535 hasRelatedWork W2999121911 @default.
- W4287993535 hasRelatedWork W3000408518 @default.
- W4287993535 hasRelatedWork W4289406433 @default.
- W4287993535 isParatext "false" @default.
- W4287993535 isRetracted "false" @default.
- W4287993535 workType "article" @default.