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Mathematics > Combinatorics

arXiv:2404.02551 (math)
[Submitted on 3 Apr 2024]

Title:Degree Sequence Optimization and Extremal Degree Enumerators

Authors:Shmuel Onn
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Abstract:The degree sequence optimization problem is to find a subgraph of a given graph which maximizes the sum of given functions evaluated at the subgraph degrees. Here we study this problem by replacing degree sequences, via suitable nonlinear transformations, by suitable degree enumerators, and we introduce suitable degree enumerator polytopes.
We characterize their vertices, that is, the extremal degree enumerators, for complete graphs and some complete bipartite graphs, and use these characterizations to obtain simpler and faster algorithms for optimization over degree sequences for such graphs.
Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM); Data Structures and Algorithms (cs.DS); Optimization and Control (math.OC)
MSC classes: 05A, 15A, 51M, 52A, 52B, 52C, 62H, 68Q, 68R, 68U, 68W, 90B, 90C
Cite as: arXiv:2404.02551 [math.CO]
  (or arXiv:2404.02551v1 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.2404.02551

Submission history

From: Shmuel Onn [view email]
[v1] Wed, 3 Apr 2024 08:18:30 UTC (12 KB)
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