The edge intersection graphs of paths in a tree

Martin Charles Golumbic; Robert E. Jamison

doi:10.1016/0095-8956(85)90088-7

The edge intersection graphs of paths in a tree

Martin Charles Golumbic, Robert E. Jamison

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

Abstract

The class of edge intersection graphs of a collection of paths in a tree (EPT graphs) is investigated, where two paths edge intersect if they share an edge. The cliques of an EPT graph are characterized and shown to have strong Helly number 4. From this it is demonstrated that the problem of finding a maximum clique of an EPT graph can be solved in polynomial time. It is shown that the strong perfect graph conjecture holds for EPT graphs. Further complexity results follow from the observation that every line graph is an EPT graph. The class of EPT graphs is equivalent to the class of fundamental cycle graphs.

Original language	English
Pages (from-to)	8-22
Number of pages	15
Journal	Journal of Combinatorial Theory. Series B
Volume	38
Issue number	1
DOIs	https://doi.org/10.1016/0095-8956(85)90088-7
State	Published - Feb 1985
Externally published	Yes

Bibliographical note

Funding Information:
research was supported in part by NSF Grant BP-801 8

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Access to Document

10.1016/0095-8956(85)90088-7

Cite this

@article{d769556e5cdf46d78b97cd528e0e6c89,

title = "The edge intersection graphs of paths in a tree",

abstract = "The class of edge intersection graphs of a collection of paths in a tree (EPT graphs) is investigated, where two paths edge intersect if they share an edge. The cliques of an EPT graph are characterized and shown to have strong Helly number 4. From this it is demonstrated that the problem of finding a maximum clique of an EPT graph can be solved in polynomial time. It is shown that the strong perfect graph conjecture holds for EPT graphs. Further complexity results follow from the observation that every line graph is an EPT graph. The class of EPT graphs is equivalent to the class of fundamental cycle graphs.",

author = "Golumbic, {Martin Charles} and Jamison, {Robert E.}",

note = "Funding Information: research was supported in part by NSF Grant BP-801 8",

year = "1985",

month = feb,

doi = "10.1016/0095-8956(85)90088-7",

language = "English",

volume = "38",

pages = "8--22",

journal = "Journal of Combinatorial Theory. Series B",

issn = "0095-8956",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - The edge intersection graphs of paths in a tree

AU - Golumbic, Martin Charles

AU - Jamison, Robert E.

N1 - Funding Information: research was supported in part by NSF Grant BP-801 8

PY - 1985/2

Y1 - 1985/2

N2 - The class of edge intersection graphs of a collection of paths in a tree (EPT graphs) is investigated, where two paths edge intersect if they share an edge. The cliques of an EPT graph are characterized and shown to have strong Helly number 4. From this it is demonstrated that the problem of finding a maximum clique of an EPT graph can be solved in polynomial time. It is shown that the strong perfect graph conjecture holds for EPT graphs. Further complexity results follow from the observation that every line graph is an EPT graph. The class of EPT graphs is equivalent to the class of fundamental cycle graphs.

AB - The class of edge intersection graphs of a collection of paths in a tree (EPT graphs) is investigated, where two paths edge intersect if they share an edge. The cliques of an EPT graph are characterized and shown to have strong Helly number 4. From this it is demonstrated that the problem of finding a maximum clique of an EPT graph can be solved in polynomial time. It is shown that the strong perfect graph conjecture holds for EPT graphs. Further complexity results follow from the observation that every line graph is an EPT graph. The class of EPT graphs is equivalent to the class of fundamental cycle graphs.

UR - http://www.scopus.com/inward/record.url?scp=0004425381&partnerID=8YFLogxK

U2 - 10.1016/0095-8956(85)90088-7

DO - 10.1016/0095-8956(85)90088-7

M3 - Article

AN - SCOPUS:0004425381

SN - 0095-8956

VL - 38

SP - 8

EP - 22

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

IS - 1

ER -

The edge intersection graphs of paths in a tree

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this