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Overlaying a hypergraph with a graph with bounded maximum degree

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Abstract

Let G and H be respectively a graph and a hypergraph defined on a same set of vertices, and let F be a fixed graph. We say that G F-overlays a hyperedge S of H if F is a spanning subgraph of the subgraph of G induced by S, and that it F-overlays H if it F-overlays every hyperedge of H. Motivated by structural biology, we study the computational complexity of two problems. The first problem, (∆ ≤ k) F-Overlay, consists in deciding whether there is a graph with maximum degree at most k that F-overlays a given hypergraph H. It is a particular case of the second problem Max (∆ ≤ k) F-Overlay, which takes a hypergraph H and an integer s as input, and consists in deciding whether there is a graph with maximum degree at most k that F-overlays at least s hyperedges of H. We give a complete polynomial/N P-complete dichotomy for the Max (∆ ≤ k)-F-Overlay problems depending on the pairs (F, k), and establish the complexity of (∆ ≤ k) F-Overlay for many pairs (F, k).
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Dates and versions

hal-03035849 , version 1 (02-12-2020)

Identifiers

  • HAL Id : hal-03035849 , version 1

Cite

Frédéric Havet, Dorian Mazauric, Viet-Ha Nguyen, Rémi Watrigant. Overlaying a hypergraph with a graph with bounded maximum degree. CALDAM 2020 - 6th Annual International Conference on Algorithms and Discrete Applied Mathematics, Feb 2020, Hyderabad, India. ⟨hal-03035849⟩
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