2,163 research outputs found
A simple linear time algorithm for the locally connected spanning tree problem on maximal planar chordal graphs
A locally connected spanning tree (LCST) T of a graph G is a spanning tree of G such that, for each node, its neighborhood in T induces a connected sub- graph in G. The problem of determining whether a graph contains an LCST or not has been proved to be NP-complete, even if the graph is planar or chordal. The main result of this paper is a simple linear time algorithm that, given a maximal planar chordal graph, determines in linear time whether it contains an LCST or not, and produces one if it exists. We give an anal- ogous result for the case when the input graph is a maximal outerplanar graph
Local Certification of Some Geometric Intersection Graph Classes
In the context of distributed certification, the recognition of graph classes
has started to be intensively studied. For instance, different results related
to the recognition of planar, bounded tree-width and -minor free graphs have
been recently obtained. The goal of the present work is to design compact
certificates for the local recognition of relevant geometric intersection graph
classes, namely interval, chordal, circular arc, trapezoid and permutation.
More precisely, we give proof labeling schemes recognizing each of these
classes with logarithmic-sized certificates. We also provide tight logarithmic
lower bounds on the size of the certificates on the proof labeling schemes for
the recognition of any of the aforementioned geometric intersection graph
classes
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