Bar-Noy, Amotz
[VerfasserIn];
Peleg, David
[VerfasserIn];
Rawitz, Dror
[VerfasserIn];
Yehezkel, Elad
[VerfasserIn]
;
Amotz Bar-Noy and David Peleg and Dror Rawitz and Elad Yehezkel
[MitwirkendeR]
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Beschreibung:
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.