Matches in SemOpenAlex for { <https://semopenalex.org/work/W3083450584> ?p ?o ?g. }
Showing items 1 to 72 of
72
with 100 items per page.
- W3083450584 abstract "A vertex coloring of a given graph $G$ is conflict-free if the closed neighborhood of every vertex contains a unique color (i.e. a color appearing only once in the neighborhood). The minimum number of colors in such a coloring is the conflict-free chromatic number of $G$, denoted $chi_{CF}(G)$. What is the maximum possible conflict-free chromatic number of a graph with a given maximum degree $Delta$? Trivially, $chi_{CF}(G)leq chi(G)leq Delta+1$, but it is far from optimal - due to results of Glebov, Szabo and Tardos, and of Bhyravarapu, Kalyanasundaram and Mathew, the answer in known to be $Thetaleft(ln^2Deltaright)$. We show that the answer to the same question in the class of line graphs is $Thetaleft(lnDeltaright)$ - that is, the extremal value of the conflict-free chromatic index among graphs with maximum degree $Delta$ is much smaller than the one for conflict-free chromatic number. The same result for $chi_{CF}(G)$ is also provided in the class of near regular graphs, i.e. graphs with minimum degree $delta geq alpha Delta$." @default.
- W3083450584 created "2020-09-11" @default.
- W3083450584 creator A5009715410 @default.
- W3083450584 creator A5066501857 @default.
- W3083450584 date "2020-09-04" @default.
- W3083450584 modified "2023-10-02" @default.
- W3083450584 title "Conflict-free chromatic number vs conflict-free chromatic index" @default.
- W3083450584 cites W157196075 @default.
- W3083450584 cites W1826123464 @default.
- W3083450584 cites W1984697505 @default.
- W3083450584 cites W2014924232 @default.
- W3083450584 cites W2071386577 @default.
- W3083450584 cites W2112505974 @default.
- W3083450584 cites W2119116325 @default.
- W3083450584 cites W2136009350 @default.
- W3083450584 cites W2948265309 @default.
- W3083450584 cites W3011505031 @default.
- W3083450584 hasPublicationYear "2020" @default.
- W3083450584 type Work @default.
- W3083450584 sameAs 3083450584 @default.
- W3083450584 citedByCount "1" @default.
- W3083450584 countsByYear W30834505842020 @default.
- W3083450584 crossrefType "posted-content" @default.
- W3083450584 hasAuthorship W3083450584A5009715410 @default.
- W3083450584 hasAuthorship W3083450584A5066501857 @default.
- W3083450584 hasConcept C114614502 @default.
- W3083450584 hasConcept C118615104 @default.
- W3083450584 hasConcept C121332964 @default.
- W3083450584 hasConcept C132525143 @default.
- W3083450584 hasConcept C196956537 @default.
- W3083450584 hasConcept C24890656 @default.
- W3083450584 hasConcept C2775997480 @default.
- W3083450584 hasConcept C2983226441 @default.
- W3083450584 hasConcept C33923547 @default.
- W3083450584 hasConcept C80899671 @default.
- W3083450584 hasConceptScore W3083450584C114614502 @default.
- W3083450584 hasConceptScore W3083450584C118615104 @default.
- W3083450584 hasConceptScore W3083450584C121332964 @default.
- W3083450584 hasConceptScore W3083450584C132525143 @default.
- W3083450584 hasConceptScore W3083450584C196956537 @default.
- W3083450584 hasConceptScore W3083450584C24890656 @default.
- W3083450584 hasConceptScore W3083450584C2775997480 @default.
- W3083450584 hasConceptScore W3083450584C2983226441 @default.
- W3083450584 hasConceptScore W3083450584C33923547 @default.
- W3083450584 hasConceptScore W3083450584C80899671 @default.
- W3083450584 hasLocation W30834505841 @default.
- W3083450584 hasOpenAccess W3083450584 @default.
- W3083450584 hasPrimaryLocation W30834505841 @default.
- W3083450584 hasRelatedWork W1561566044 @default.
- W3083450584 hasRelatedWork W1679011346 @default.
- W3083450584 hasRelatedWork W1836371877 @default.
- W3083450584 hasRelatedWork W2105531552 @default.
- W3083450584 hasRelatedWork W2247104300 @default.
- W3083450584 hasRelatedWork W2268849514 @default.
- W3083450584 hasRelatedWork W2559318442 @default.
- W3083450584 hasRelatedWork W2739099791 @default.
- W3083450584 hasRelatedWork W2762613837 @default.
- W3083450584 hasRelatedWork W2804029448 @default.
- W3083450584 hasRelatedWork W2901929679 @default.
- W3083450584 hasRelatedWork W2949417199 @default.
- W3083450584 hasRelatedWork W2950785889 @default.
- W3083450584 hasRelatedWork W2952598112 @default.
- W3083450584 hasRelatedWork W2963535564 @default.
- W3083450584 hasRelatedWork W2972140897 @default.
- W3083450584 hasRelatedWork W3012703112 @default.
- W3083450584 hasRelatedWork W3031037285 @default.
- W3083450584 hasRelatedWork W3085035574 @default.
- W3083450584 hasRelatedWork W591309253 @default.
- W3083450584 isParatext "false" @default.
- W3083450584 isRetracted "false" @default.
- W3083450584 magId "3083450584" @default.
- W3083450584 workType "article" @default.