@inproceedings{48467fd4e5bb4dda825d59bc766c00b7,

title = "Intersection Graphs of Non-crossing Paths",

abstract = "We study graph classes modeled by families of non-crossing (NC) connected sets. Two classic graph classes in this context are disk graphs and proper interval graphs. We focus on the cases when the sets are paths and the host is a tree. Forbidden induced subgraph characterizations and linear time certifying recognition algorithms are given for intersection graphs of NC paths of a tree (and related subclasses). For intersection graphs of NC paths of a tree, the dominating set problem is shown to be solvable in linear time. Also, each such graph is shown to have a Hamiltonian cycle if and only if it is 2-connected, and to have a Hamiltonian path if and only if its block-cutpoint tree is a path.",

keywords = "Clique trees, DOMINATING SETS, Domination, HAMILTONIAN CIRCUITS, Hamiltonicity, Non-crossing models, RECOGNITION ALGORITHM",

author = "Steven Chaplick",

note = "DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.",

year = "2019",

doi = "10.1007/978-3-030-30786-8_24",

language = "English",

isbn = "978-3-030-30785-1",

series = "Lecture Notes in Computer Science",

publisher = "Springer Nature Switzerland AG",

pages = "311--324",

editor = "I. Sau and D. Thilikos",

booktitle = "Graph-Theoretic Concepts in Computer Science. WG 2019",

}