2026-07-23T08:19:31Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:15460 2024-03-06T10:55:20Z ddc:004 open_access

Selected Neighbor Degree Forest Realization Bar-Noy, Amotz Peleg, David Rawitz, Dror Yehezkel, Elad network realization graph algorithms lower bound The classical degree realization problem is defined as follows: Given a sequence d̄ = (d_1,…,d_n) of positive integers, construct an n-vertex graph in which each vertex u_i has degree d_i (or decide that no such graph exists). In this article, we present and study the related selected neighbor degree realization problem, which requires that each vertex u_i of G has a neighbor of degree d_i. We solve the problem when G is required to be acyclic (i.e., a forest), and present a sufficient and necessary condition for a given sequence to be realizable. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Amotz Bar-Noy and David Peleg and Dror Rawitz and Elad Yehezkel 2021 Is Part Of LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2021.27 urn:nbn:de:0030-drops-154609 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.27 eng https://creativecommons.org/licenses/by/4.0/legalcode