On Building Networks with Limited Stretch Factor

Cicerone, Serafino

doi:10.1007/978-3-030-44038-1_84

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2021

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“…As a consequence, it would be interesting to determine whether the class sDH(2) can be also characterized according to generative operations (we remind that the generative properties resulted as the most fruitful for devising efficient algorithms for distance-hereditary graphs). This problem has been partially addressed in [18,19].…”

Section: Discussionmentioning

confidence: 99%

A Quasi-Hole Detection Algorithm for Recognizing k-Distance-Hereditary Graphs, with k < 2

Cicerone¹

2021

Algorithms

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Cicerone and Di Stefano defined and studied the class of k-distance-hereditary graphs, i.e., graphs where the distance in each connected induced subgraph is at most k times the distance in the whole graph. The defined graphs represent a generalization of the well known distance-hereditary graphs, which actually correspond to 1-distance-hereditary graphs. In this paper we make a step forward in the study of these new graphs by providing characterizations for the class of all the k-distance-hereditary graphs such that k<2. The new characterizations are given in terms of both forbidden subgraphs and cycle-chord properties. Such results also lead to devise a polynomial-time recognition algorithm for this kind of graph that, according to the provided characterizations, simply detects the presence of quasi-holes in any given graph.

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Section: Discussionmentioning

confidence: 99%