k-Chordal Graphs: From Cops and Robber to Compact Routing via Treewidth

@inproceedings{Kosowski2012kChordalGF,
  title={k-Chordal Graphs: From Cops and Robber to Compact Routing via Treewidth},
  author={Adrian Kosowski and Bi Li and Nicolas Nisse and Karol Suchan},
  booktitle={ICALP},
  year={2012}
}
Cops and robber games, introduced by Winkler and Nowakowski [41] and independently defined by Quilliot [43], concern a team of cops that must capture a robber moving in a graph. We consider the class of k-chordal graphs, i.e., graphs with no induced (chordless) cycle of length greater than k, k≥ 3. We prove that k−1 cops are always sufficient to capture a robber in k-chordal graphs. This leads us to our main result, a new structural decomposition for a graph class including k-chordal graphs. We… CONTINUE READING
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