Transversals of Longest Paths

Márcia R. Cerioli; Cristina G. Fernandes; Renzo Gómez; Juan Gutiérrez; Paloma T. Lima

doi:10.1016/j.endm.2017.10.024

Transversals of Longest Paths

Márcia R. Cerioli, Cristina G. Fernandes, Renzo Gómez, Juan Gutiérrez, Paloma T. Lima

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let lpt(G) be the minimum cardinality of a set of vertices that intersects all longest paths in a connected graph G. We show that, if G is a chordal graph, then lpt(G)≤max⁡{1,ω(G)−2}, where ω(G) is the size of a largest clique in G; that lpt(G)≤tw(G), where tw(G) is the treewidth of G; and that lpt(G)=1 if G is a bipartite permutation graph or a full substar graph.

Original language	English
Pages (from-to)	135-140
Number of pages	6
Journal	Electronic Notes in Discrete Mathematics
Volume	62
DOIs	https://doi.org/10.1016/j.endm.2017.10.024
State	Published - Nov 2017
Externally published	Yes

Keywords

chordal
longest path
permutation
substars
transversal
treewidth

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10.1016/j.endm.2017.10.024

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title = "Transversals of Longest Paths",

abstract = "Let lpt(G) be the minimum cardinality of a set of vertices that intersects all longest paths in a connected graph G. We show that, if G is a chordal graph, then lpt(G)≤max⁡{1,ω(G)−2}, where ω(G) is the size of a largest clique in G; that lpt(G)≤tw(G), where tw(G) is the treewidth of G; and that lpt(G)=1 if G is a bipartite permutation graph or a full substar graph.",

keywords = "chordal, longest path, permutation, substars, transversal, treewidth",

author = "Cerioli, {M{\'a}rcia R.} and Fernandes, {Cristina G.} and Renzo G{\'o}mez and Juan Guti{\'e}rrez and Lima, {Paloma T.}",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2017",

month = nov,

doi = "10.1016/j.endm.2017.10.024",

language = "English",

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journal = "Electronic Notes in Discrete Mathematics",

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T1 - Transversals of Longest Paths

AU - Cerioli, Márcia R.

AU - Fernandes, Cristina G.

AU - Gómez, Renzo

AU - Gutiérrez, Juan

AU - Lima, Paloma T.

PY - 2017/11

Y1 - 2017/11

N2 - Let lpt(G) be the minimum cardinality of a set of vertices that intersects all longest paths in a connected graph G. We show that, if G is a chordal graph, then lpt(G)≤max⁡{1,ω(G)−2}, where ω(G) is the size of a largest clique in G; that lpt(G)≤tw(G), where tw(G) is the treewidth of G; and that lpt(G)=1 if G is a bipartite permutation graph or a full substar graph.

AB - Let lpt(G) be the minimum cardinality of a set of vertices that intersects all longest paths in a connected graph G. We show that, if G is a chordal graph, then lpt(G)≤max⁡{1,ω(G)−2}, where ω(G) is the size of a largest clique in G; that lpt(G)≤tw(G), where tw(G) is the treewidth of G; and that lpt(G)=1 if G is a bipartite permutation graph or a full substar graph.

KW - chordal

KW - longest path

KW - permutation

KW - substars

KW - transversal

KW - treewidth

UR - http://www.scopus.com/inward/record.url?scp=85032434324&partnerID=8YFLogxK

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DO - 10.1016/j.endm.2017.10.024

M3 - Article

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SN - 1571-0653

VL - 62

SP - 135

EP - 140

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -

Transversals of Longest Paths

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Keywords

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