Matches in SemOpenAlex for { <https://semopenalex.org/work/W3088149488> ?p ?o ?g. }
Showing items 1 to 75 of
75
with 100 items per page.
- W3088149488 endingPage "150" @default.
- W3088149488 startingPage "141" @default.
- W3088149488 abstract "Hedetniemi conjectured in 1966 that χ(G×H)=min{χ(G),χ(H)} for all graphs G and H. Here G×H is the graph with vertex set V(G)×V(H) defined by putting (x,y) and (x′,y′) adjacent if and only if xx′∈E(G) and yy′∈E(H). This conjecture received a lot of attention in the past half century. Recently, Shitov refuted this conjecture. Let p be the minimum number of vertices in a graph of odd girth 7 and fractional chromatic number greater than 3+4/(p−1). Shitov's proof shows that Hedetniemi's conjecture fails for some graphs with chromatic number about p33p. In this paper, we show that the conjecture fails already for some graphs G and H with chromatic number 3⌈p+12⌉ and with p⌈(p−1)/2⌉ and 3⌈p+12⌉(p+1)−p vertices, respectively. The currently known upper bound for p is 83. Thus Hedetniemi's conjecture fails for some graphs G and H with chromatic number 126, and with 3,403 and 10,501 vertices, respectively." @default.
- W3088149488 created "2020-10-01" @default.
- W3088149488 creator A5020969478 @default.
- W3088149488 date "2021-01-01" @default.
- W3088149488 modified "2023-09-27" @default.
- W3088149488 title "Relatively small counterexamples to Hedetniemi's conjecture" @default.
- W3088149488 cites W1483461381 @default.
- W3088149488 cites W1540614089 @default.
- W3088149488 cites W1998475227 @default.
- W3088149488 cites W2004030389 @default.
- W3088149488 cites W2022623224 @default.
- W3088149488 cites W2032331898 @default.
- W3088149488 cites W2045583023 @default.
- W3088149488 cites W2048118184 @default.
- W3088149488 cites W2095076239 @default.
- W3088149488 cites W2599950914 @default.
- W3088149488 cites W2969838569 @default.
- W3088149488 cites W2990952870 @default.
- W3088149488 cites W3102760800 @default.
- W3088149488 cites W4229970255 @default.
- W3088149488 doi "https://doi.org/10.1016/j.jctb.2020.09.005" @default.
- W3088149488 hasPublicationYear "2021" @default.
- W3088149488 type Work @default.
- W3088149488 sameAs 3088149488 @default.
- W3088149488 citedByCount "7" @default.
- W3088149488 countsByYear W30881494882020 @default.
- W3088149488 countsByYear W30881494882021 @default.
- W3088149488 countsByYear W30881494882022 @default.
- W3088149488 countsByYear W30881494882023 @default.
- W3088149488 crossrefType "journal-article" @default.
- W3088149488 hasAuthorship W3088149488A5020969478 @default.
- W3088149488 hasBestOaLocation W30881494882 @default.
- W3088149488 hasConcept C114614502 @default.
- W3088149488 hasConcept C118615104 @default.
- W3088149488 hasConcept C132525143 @default.
- W3088149488 hasConcept C134306372 @default.
- W3088149488 hasConcept C162838799 @default.
- W3088149488 hasConcept C196956537 @default.
- W3088149488 hasConcept C2780990831 @default.
- W3088149488 hasConcept C33923547 @default.
- W3088149488 hasConcept C77553402 @default.
- W3088149488 hasConcept C80899671 @default.
- W3088149488 hasConceptScore W3088149488C114614502 @default.
- W3088149488 hasConceptScore W3088149488C118615104 @default.
- W3088149488 hasConceptScore W3088149488C132525143 @default.
- W3088149488 hasConceptScore W3088149488C134306372 @default.
- W3088149488 hasConceptScore W3088149488C162838799 @default.
- W3088149488 hasConceptScore W3088149488C196956537 @default.
- W3088149488 hasConceptScore W3088149488C2780990831 @default.
- W3088149488 hasConceptScore W3088149488C33923547 @default.
- W3088149488 hasConceptScore W3088149488C77553402 @default.
- W3088149488 hasConceptScore W3088149488C80899671 @default.
- W3088149488 hasFunder F4320321001 @default.
- W3088149488 hasFunder F4320321106 @default.
- W3088149488 hasLocation W30881494881 @default.
- W3088149488 hasLocation W30881494882 @default.
- W3088149488 hasOpenAccess W3088149488 @default.
- W3088149488 hasPrimaryLocation W30881494881 @default.
- W3088149488 hasRelatedWork W2067688212 @default.
- W3088149488 hasRelatedWork W2293240310 @default.
- W3088149488 hasRelatedWork W2347260277 @default.
- W3088149488 hasRelatedWork W2422813311 @default.
- W3088149488 hasRelatedWork W2952342369 @default.
- W3088149488 hasRelatedWork W3207412727 @default.
- W3088149488 hasRelatedWork W4243250875 @default.
- W3088149488 hasRelatedWork W4286901599 @default.
- W3088149488 hasRelatedWork W4287018471 @default.
- W3088149488 hasRelatedWork W4291863732 @default.
- W3088149488 hasVolume "146" @default.
- W3088149488 isParatext "false" @default.
- W3088149488 isRetracted "false" @default.
- W3088149488 magId "3088149488" @default.
- W3088149488 workType "article" @default.