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Hardness and efficiency on minimizing maximum distances in spanning trees
Theoretical Computer Science ( IF 0.747 ) Pub Date : 2020-06-29 , DOI: 10.1016/j.tcs.2020.06.012
Fernanda Couto; Luís Felipe I. Cunha

The t-admissibility problem aims to decide whether a graph G has a spanning tree T in which the distance between any two adjacent vertices of G is at most t. Regarding its optimization version, the smallest t for which G is t-admissible is the stretch index of G, denoted by σT(G). The problem of deciding whether σT(G)≤t, t≥4 is NP-complete and polynomial-time solvable for t=2. However, deciding if t=3 is an open problem. We determine 3-admissible graph classes by studying graphs with few P4's, and we partially classify the P vs NP-complete dichotomy of the t-admissibility problem for (k,ℓ)-graphs. These graph classes generalize some others in which the computational complexity of the t-admissibility problem was already determined. Moreover, we determine the stretch index for cycle-power graphs and for (2,1)-chordal graphs, which are subclasses of (k,ℓ)-graphs and the t-admissibility problem is NP-complete.
更新日期:2020-06-29

 

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