Abstract
A graph is k-degree-anonymous if for each vertex there are at least \(k-1 \) other vertices of the same degree in the graph. Min Anonymous-Edge-Rotation asks for a given graph G and a positive integer k to find a minimum number of edge rotations that transform G into a k-degree-anonymous graph. In this paper, we establish sufficient conditions for an input graph and k ensuring that a solution for the problem exists. We also prove that the Min Anonymous-Edge-Rotation problem is NP-hard even for \(k=n/3\), where n is the order of a graph. On the positive side, we argue that under some constraints on the number of edges in a graph and k, Min Anonymous-Edge-Rotation is polynomial-time 2-approximable. Moreover, we show that the problem is solvable in polynomial time for any graph when \(k=n\) and for trees when \(k=\theta (n)\).
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Bazgan, C., Cazals, P., Chlebíková, J. (2020). How to Get a Degree-Anonymous Graph Using Minimum Number of Edge Rotations. In: Wu, W., Zhang, Z. (eds) Combinatorial Optimization and Applications. COCOA 2020. Lecture Notes in Computer Science(), vol 12577. Springer, Cham. https://doi.org/10.1007/978-3-030-64843-5_17
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DOI: https://doi.org/10.1007/978-3-030-64843-5_17
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