A DE-pair (ODE-pair) in a graph consists of two disjoint subsets of vertices with the same closed neighborhood (open neighborhood). We consider the question of determining the smallest and largest subsets over all such pairs. We provide sharp bounds on these for general graphs and for trees, and show that the associated parameters are computable for trees but intractable in general.
机构:
Slovak Univ Technol Bratislava, Fac Civil Engn, Dept Math, Bratislava, SlovakiaSlovak Univ Technol Bratislava, Fac Civil Engn, Dept Math, Bratislava, Slovakia
Knor, Martin
Skrekovski, Riste
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Univ Ljubljana, FMF, Koper, Slovenia
Fac Informat Studies, Novo Mesto, Slovenia
Univ Primorska, FAMNIT, Koper, SloveniaSlovak Univ Technol Bratislava, Fac Civil Engn, Dept Math, Bratislava, Slovakia
Skrekovski, Riste
Tepeh, Aleksandra
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Fac Informat Studies, Novo Mesto, Slovenia
Univ Maribor, Fac Elect Engn & Comp Sci, Koroska Cesta 46, SI-2000 Maribor, SloveniaSlovak Univ Technol Bratislava, Fac Civil Engn, Dept Math, Bratislava, Slovakia