Matches in SemOpenAlex for { <https://semopenalex.org/work/W1489491179> ?p ?o ?g. }
Showing items 1 to 71 of
71
with 100 items per page.
- W1489491179 abstract "An orthogonal coloring of a graph $G$ is a pair ${c_1,c_2}$ of proper colorings of $G$, having the property that if two vertices are colored with the same color in $c_1$, then they must have distinct colors in $c_2$. The notion of orthogonal colorings is strongly related to the notion of orthogonal Latin squares. The orthogonal chromatic number of $G$, denoted by $Ochi(G)$, is the minimum possible number of colors used in an orthogonal coloring of $G$. If $G$ has $n$ vertices, then the definition implies that $leftlceil sqrt{n} , rightrceil leq Ochi(G) leq n$. $G$ is said to have an optimal orthogonal coloring if $Ochi(G) = leftlceil sqrt{n} , rightrceil$. If, in addition, $n$ is an integer square, then we say that $G$ has a perfect orthogonal coloring, since for any two colors $x$ and $y$, there is exactly one vertex colored by $x$ in $c_1$ and by $y$ in $c_2$. The purpose of this paper is to study the parameter $Ochi(G)$ and supply upper bounds to it which depend on other graph parameters such as the maximum degree and the chromatic number. We also study the structure of graphs having an optimal or perfect orthogonal coloring, and show that several classes of graphs always have an optimal or perfect orthogonal coloring. We also consider the strong version of orthogonal colorings, where no vertex may receive the same color in both colorings." @default.
- W1489491179 created "2016-06-24" @default.
- W1489491179 creator A5000697501 @default.
- W1489491179 creator A5026016357 @default.
- W1489491179 date "1998-12-06" @default.
- W1489491179 modified "2023-10-01" @default.
- W1489491179 title "Orthogonal Colorings of Graphs" @default.
- W1489491179 cites W1510730180 @default.
- W1489491179 cites W1990479896 @default.
- W1489491179 cites W2010354676 @default.
- W1489491179 doi "https://doi.org/10.37236/1437" @default.
- W1489491179 hasPublicationYear "1998" @default.
- W1489491179 type Work @default.
- W1489491179 sameAs 1489491179 @default.
- W1489491179 citedByCount "2" @default.
- W1489491179 countsByYear W14894911792022 @default.
- W1489491179 crossrefType "journal-article" @default.
- W1489491179 hasAuthorship W1489491179A5000697501 @default.
- W1489491179 hasAuthorship W1489491179A5026016357 @default.
- W1489491179 hasBestOaLocation W14894911791 @default.
- W1489491179 hasConcept C105795698 @default.
- W1489491179 hasConcept C114614502 @default.
- W1489491179 hasConcept C118615104 @default.
- W1489491179 hasConcept C123809776 @default.
- W1489491179 hasConcept C132525143 @default.
- W1489491179 hasConcept C149530733 @default.
- W1489491179 hasConcept C158319403 @default.
- W1489491179 hasConcept C196956537 @default.
- W1489491179 hasConcept C199594403 @default.
- W1489491179 hasConcept C203776342 @default.
- W1489491179 hasConcept C21642379 @default.
- W1489491179 hasConcept C33923547 @default.
- W1489491179 hasConcept C38767284 @default.
- W1489491179 hasConcept C42632107 @default.
- W1489491179 hasConcept C80899671 @default.
- W1489491179 hasConcept C83469408 @default.
- W1489491179 hasConceptScore W1489491179C105795698 @default.
- W1489491179 hasConceptScore W1489491179C114614502 @default.
- W1489491179 hasConceptScore W1489491179C118615104 @default.
- W1489491179 hasConceptScore W1489491179C123809776 @default.
- W1489491179 hasConceptScore W1489491179C132525143 @default.
- W1489491179 hasConceptScore W1489491179C149530733 @default.
- W1489491179 hasConceptScore W1489491179C158319403 @default.
- W1489491179 hasConceptScore W1489491179C196956537 @default.
- W1489491179 hasConceptScore W1489491179C199594403 @default.
- W1489491179 hasConceptScore W1489491179C203776342 @default.
- W1489491179 hasConceptScore W1489491179C21642379 @default.
- W1489491179 hasConceptScore W1489491179C33923547 @default.
- W1489491179 hasConceptScore W1489491179C38767284 @default.
- W1489491179 hasConceptScore W1489491179C42632107 @default.
- W1489491179 hasConceptScore W1489491179C80899671 @default.
- W1489491179 hasConceptScore W1489491179C83469408 @default.
- W1489491179 hasIssue "1" @default.
- W1489491179 hasLocation W14894911791 @default.
- W1489491179 hasOpenAccess W1489491179 @default.
- W1489491179 hasPrimaryLocation W14894911791 @default.
- W1489491179 hasRelatedWork W1489491179 @default.
- W1489491179 hasRelatedWork W1974068132 @default.
- W1489491179 hasRelatedWork W2042876012 @default.
- W1489491179 hasRelatedWork W2056389765 @default.
- W1489491179 hasRelatedWork W2151059773 @default.
- W1489491179 hasRelatedWork W2353563269 @default.
- W1489491179 hasRelatedWork W2356152809 @default.
- W1489491179 hasRelatedWork W2365539738 @default.
- W1489491179 hasRelatedWork W2376326396 @default.
- W1489491179 hasRelatedWork W4288274833 @default.
- W1489491179 hasVolume "6" @default.
- W1489491179 isParatext "false" @default.
- W1489491179 isRetracted "false" @default.
- W1489491179 magId "1489491179" @default.
- W1489491179 workType "article" @default.