FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3042824509> ?p ?o ?g. }

• W3042824509 abstract "A plane topological graph $G=(V,E)$ is a graph drawn in the plane whose vertices are points in the plane and whose edges are simple curves that do not intersect, except at their endpoints. Given a plane topological graph $G=(V,E)$ and a set $C_G$ of parity constraints, in which every vertex has assigned a parity constraint on its degree, either even or odd, we say that $G$ is emph{topologically augmentable} to meet $C_G$ if there exits a plane topological graph $H$ on the same set of vertices, such that $G$ and $H$ are edge-disjoint and their union is a plane topological graph that meets all parity constraints. In this paper, we prove that the problem of deciding if a plane topological graph is topologically augmentable to meet parity constraints is $mathcal{NP}$-complete, even if the set of vertices that must change their parities is $V$ or the set of vertices with odd degree. In particular, deciding if a plane topological graph can be augmented to a Eulerian plane topological graph is $mathcal{NP}$-complete. Analogous complexity results are obtained, when the augmentation must be done by a plane topological perfect matching between the vertices not meeting their parities. We extend these hardness results to planar graphs, when the augmented graph must be planar, and to plane geometric graphs (plane topological graphs whose edges are straight-line segments). In addition, when it is required that the augmentation is made by a plane geometric perfect matching between the vertices not meeting their parities, we also prove that this augmentation problem is $mathcal{NP}$-complete for plane geometric trees and paths. For the particular family of maximal outerplane graphs, we characterize maximal outerplane graphs that are topological augmentable to satisfy a set of parity constraints." @default.
• W3042824509 created "2020-07-23" @default.
• W3042824509 creator A5017314292 @default.
• W3042824509 creator A5038889056 @default.
• W3042824509 creator A5068857927 @default.
• W3042824509 creator A5078491368 @default.
• W3042824509 date "2020-12-01" @default.
• W3042824509 modified "2023-10-01" @default.
• W3042824509 title "Plane augmentation of plane graphs to meet parity constraints" @default.
• W3042824509 cites W1501403775 @default.
• W3042824509 cites W1972701463 @default.
• W3042824509 cites W1974848406 @default.
• W3042824509 cites W1979888220 @default.
• W3042824509 cites W1980097246 @default.
• W3042824509 cites W1981160608 @default.
• W3042824509 cites W200506746 @default.
• W3042824509 cites W2008562682 @default.
• W3042824509 cites W2011374244 @default.
• W3042824509 cites W2020837584 @default.
• W3042824509 cites W2022451101 @default.
• W3042824509 cites W2026720321 @default.
• W3042824509 cites W2027758271 @default.
• W3042824509 cites W2035543139 @default.
• W3042824509 cites W2035591976 @default.
• W3042824509 cites W2060069351 @default.
• W3042824509 cites W2062440435 @default.
• W3042824509 cites W2063013286 @default.
• W3042824509 cites W2064011321 @default.
• W3042824509 cites W2064284095 @default.
• W3042824509 cites W2066577300 @default.
• W3042824509 cites W2081463432 @default.
• W3042824509 cites W2082388593 @default.
• W3042824509 cites W2116031575 @default.
• W3042824509 cites W2138849026 @default.
• W3042824509 cites W2139199176 @default.
• W3042824509 cites W2287418059 @default.
• W3042824509 cites W2612435103 @default.
• W3042824509 cites W2783640348 @default.
• W3042824509 cites W2792250381 @default.
• W3042824509 cites W3200272371 @default.
• W3042824509 doi "https://doi.org/10.1016/j.amc.2020.125513" @default.
• W3042824509 hasPublicationYear "2020" @default.
• W3042824509 type Work @default.
• W3042824509 sameAs 3042824509 @default.
• W3042824509 citedByCount "0" @default.
• W3042824509 crossrefType "journal-article" @default.
• W3042824509 hasAuthorship W3042824509A5017314292 @default.
• W3042824509 hasAuthorship W3042824509A5038889056 @default.
• W3042824509 hasAuthorship W3042824509A5068857927 @default.
• W3042824509 hasAuthorship W3042824509A5078491368 @default.
• W3042824509 hasBestOaLocation W30428245092 @default.
• W3042824509 hasConcept C101837359 @default.
• W3042824509 hasConcept C109214941 @default.
• W3042824509 hasConcept C114614502 @default.
• W3042824509 hasConcept C118615104 @default.
• W3042824509 hasConcept C121332964 @default.
• W3042824509 hasConcept C132525143 @default.
• W3042824509 hasConcept C184720557 @default.
• W3042824509 hasConcept C2777151079 @default.
• W3042824509 hasConcept C33923547 @default.
• W3042824509 hasConcept C8764922 @default.
• W3042824509 hasConceptScore W3042824509C101837359 @default.
• W3042824509 hasConceptScore W3042824509C109214941 @default.
• W3042824509 hasConceptScore W3042824509C114614502 @default.
• W3042824509 hasConceptScore W3042824509C118615104 @default.
• W3042824509 hasConceptScore W3042824509C121332964 @default.
• W3042824509 hasConceptScore W3042824509C132525143 @default.
• W3042824509 hasConceptScore W3042824509C184720557 @default.
• W3042824509 hasConceptScore W3042824509C2777151079 @default.
• W3042824509 hasConceptScore W3042824509C33923547 @default.
• W3042824509 hasConceptScore W3042824509C8764922 @default.
• W3042824509 hasLocation W30428245091 @default.
• W3042824509 hasLocation W30428245092 @default.
• W3042824509 hasLocation W30428245093 @default.
• W3042824509 hasOpenAccess W3042824509 @default.
• W3042824509 hasPrimaryLocation W30428245091 @default.
• W3042824509 hasRelatedWork W11035599 @default.
• W3042824509 hasRelatedWork W25019750 @default.
• W3042824509 hasRelatedWork W3467672 @default.
• W3042824509 hasRelatedWork W52966705 @default.
• W3042824509 hasRelatedWork W54213734 @default.
• W3042824509 hasRelatedWork W54567006 @default.
• W3042824509 hasRelatedWork W58939658 @default.
• W3042824509 hasRelatedWork W606113 @default.
• W3042824509 hasRelatedWork W63325702 @default.
• W3042824509 hasRelatedWork W64951736 @default.
• W3042824509 isParatext "false" @default.
• W3042824509 isRetracted "false" @default.
• W3042824509 magId "3042824509" @default.
• W3042824509 workType "article" @default.