Matches in SemOpenAlex for { <https://semopenalex.org/work/W3039291421> ?p ?o ?g. }
Showing items 1 to 86 of
86
with 100 items per page.
- W3039291421 abstract "We prove several results on coloring squares of planar graphs without 4-cycles. First, we show that if G is such a graph, then G2 is (Δ(G) + 72)-degenerate. This implies an upper bound of Δ(G) ∣ 73 on the chromatic number of G2 as well as on several variants of the chromatic number such as the list-chromatic number, paint number, Alon-Tarsi number, and correspondence chromatic number. We also show that if Δ(G) is sufficiently large, then the upper bounds on each of these parameters of G2 can all be lowered to Δ(G) + 2 (which is best possible). To complement these results, we show that 4-cycles are unique in having this property. Specifically, let S be a finite list of positive integers, with 4 ∉ S. For each constant C, we construct a planar graph Gs,c with no cycle with length in S, but for which χ(G2) >Δ(Gs,c) + C." @default.
- W3039291421 created "2020-07-10" @default.
- W3039291421 creator A5025173209 @default.
- W3039291421 creator A5064235428 @default.
- W3039291421 creator A5089101660 @default.
- W3039291421 date "2020-07-06" @default.
- W3039291421 modified "2023-09-25" @default.
- W3039291421 title "Degeneracy and Colorings of Squares of Planar Graphs without 4-Cycles" @default.
- W3039291421 cites W1515228725 @default.
- W3039291421 cites W1994856976 @default.
- W3039291421 cites W2028038654 @default.
- W3039291421 cites W2035278325 @default.
- W3039291421 cites W2072414205 @default.
- W3039291421 cites W2114523418 @default.
- W3039291421 cites W2293855371 @default.
- W3039291421 cites W2559217904 @default.
- W3039291421 cites W2963534041 @default.
- W3039291421 cites W2963895478 @default.
- W3039291421 doi "https://doi.org/10.1007/s00493-019-4014-3" @default.
- W3039291421 hasPublicationYear "2020" @default.
- W3039291421 type Work @default.
- W3039291421 sameAs 3039291421 @default.
- W3039291421 citedByCount "0" @default.
- W3039291421 crossrefType "journal-article" @default.
- W3039291421 hasAuthorship W3039291421A5025173209 @default.
- W3039291421 hasAuthorship W3039291421A5064235428 @default.
- W3039291421 hasAuthorship W3039291421A5089101660 @default.
- W3039291421 hasBestOaLocation W30392914212 @default.
- W3039291421 hasConcept C101837359 @default.
- W3039291421 hasConcept C104317684 @default.
- W3039291421 hasConcept C112313634 @default.
- W3039291421 hasConcept C114614502 @default.
- W3039291421 hasConcept C118615104 @default.
- W3039291421 hasConcept C121332964 @default.
- W3039291421 hasConcept C127716648 @default.
- W3039291421 hasConcept C132525143 @default.
- W3039291421 hasConcept C134306372 @default.
- W3039291421 hasConcept C185592680 @default.
- W3039291421 hasConcept C188082640 @default.
- W3039291421 hasConcept C196956537 @default.
- W3039291421 hasConcept C2777727622 @default.
- W3039291421 hasConcept C33923547 @default.
- W3039291421 hasConcept C55493867 @default.
- W3039291421 hasConcept C60644358 @default.
- W3039291421 hasConcept C62520636 @default.
- W3039291421 hasConcept C72319582 @default.
- W3039291421 hasConcept C77553402 @default.
- W3039291421 hasConcept C86803240 @default.
- W3039291421 hasConceptScore W3039291421C101837359 @default.
- W3039291421 hasConceptScore W3039291421C104317684 @default.
- W3039291421 hasConceptScore W3039291421C112313634 @default.
- W3039291421 hasConceptScore W3039291421C114614502 @default.
- W3039291421 hasConceptScore W3039291421C118615104 @default.
- W3039291421 hasConceptScore W3039291421C121332964 @default.
- W3039291421 hasConceptScore W3039291421C127716648 @default.
- W3039291421 hasConceptScore W3039291421C132525143 @default.
- W3039291421 hasConceptScore W3039291421C134306372 @default.
- W3039291421 hasConceptScore W3039291421C185592680 @default.
- W3039291421 hasConceptScore W3039291421C188082640 @default.
- W3039291421 hasConceptScore W3039291421C196956537 @default.
- W3039291421 hasConceptScore W3039291421C2777727622 @default.
- W3039291421 hasConceptScore W3039291421C33923547 @default.
- W3039291421 hasConceptScore W3039291421C55493867 @default.
- W3039291421 hasConceptScore W3039291421C60644358 @default.
- W3039291421 hasConceptScore W3039291421C62520636 @default.
- W3039291421 hasConceptScore W3039291421C72319582 @default.
- W3039291421 hasConceptScore W3039291421C77553402 @default.
- W3039291421 hasConceptScore W3039291421C86803240 @default.
- W3039291421 hasLocation W30392914211 @default.
- W3039291421 hasLocation W30392914212 @default.
- W3039291421 hasOpenAccess W3039291421 @default.
- W3039291421 hasPrimaryLocation W30392914211 @default.
- W3039291421 hasRelatedWork W13416703 @default.
- W3039291421 hasRelatedWork W18873129 @default.
- W3039291421 hasRelatedWork W29624228 @default.
- W3039291421 hasRelatedWork W32160485 @default.
- W3039291421 hasRelatedWork W32916381 @default.
- W3039291421 hasRelatedWork W39112444 @default.
- W3039291421 hasRelatedWork W43632284 @default.
- W3039291421 hasRelatedWork W59058852 @default.
- W3039291421 hasRelatedWork W63101354 @default.
- W3039291421 hasRelatedWork W43987413 @default.
- W3039291421 isParatext "false" @default.
- W3039291421 isRetracted "false" @default.
- W3039291421 magId "3039291421" @default.
- W3039291421 workType "article" @default.