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Selected Neighbor Degree Forest Realization

Authors Amotz Bar-Noy, David Peleg , Dror Rawitz, Elad Yehezkel

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Amotz Bar-Noy
  • City University of New York (CUNY), NY, USA
David Peleg
  • Weizmann Institute of Science, Rehovot, Israel
Dror Rawitz
  • Bar Ilan University, Ramat-Gan, Israel
Elad Yehezkel
  • Weizmann Institute of Science, Rehovot, Israel

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Amotz Bar-Noy, David Peleg, Dror Rawitz, and Elad Yehezkel. Selected Neighbor Degree Forest Realization. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 27:1-27:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • network realization
  • graph algorithms
  • lower bound


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