Intersection Graphs of Non-crossing Paths

Steven Chaplick

doi:10.1007/978-3-030-30786-8_24

Intersection Graphs of Non-crossing Paths

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

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.

Original language	English
Title of host publication	Graph-Theoretic Concepts in Computer Science. WG 2019
Editors	I. Sau, D. Thilikos
Pages	311-324
Number of pages	14
DOIs	https://doi.org/10.1007/978-3-030-30786-8_24
Publication status	Published - 2019
Externally published	Yes

Publication series

Series	Lecture Notes in Computer Science
Volume	11789
ISSN	0302-9743

Keywords

Clique trees
DOMINATING SETS
Domination
HAMILTONIAN CIRCUITS
Hamiltonicity
Non-crossing models
RECOGNITION ALGORITHM

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10.1007/978-3-030-30786-8_24

1 Article

Intersection graphs of non-crossing paths
Chaplick, S., 2023, In: Discrete Mathematics. 346, 8, 113498.
Research output: Contribution to journal › Article › Academic › peer-review

Open Access

Cite this

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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",

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PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Clique trees

KW - DOMINATING SETS

KW - Domination

KW - HAMILTONIAN CIRCUITS

KW - Hamiltonicity

KW - Non-crossing models

KW - RECOGNITION ALGORITHM

U2 - 10.1007/978-3-030-30786-8_24

DO - 10.1007/978-3-030-30786-8_24

M3 - Conference article in proceeding

SN - 978-3-030-30785-1

T3 - Lecture Notes in Computer Science

SP - 311

EP - 324

BT - Graph-Theoretic Concepts in Computer Science. WG 2019

A2 - Sau, I.

A2 - Thilikos, D.

ER -

Intersection Graphs of Non-crossing Paths

Abstract

Publication series

Keywords

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Research output

Intersection graphs of non-crossing paths

Cite this