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dc.contributor.author
Tondato, Silvia Beatriz
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dc.contributor.author
Gutierrez, Marisa
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dc.date.available
2018-08-13T20:01:22Z
dc.date.issued
2016-06
dc.identifier.citation
Tondato, Silvia Beatriz; Gutierrez, Marisa; On rooted directed path graphs; Unión Matemática Argentina; Revista de la Unión Matemática Argentina; 57; 1; 6-2016; 114-144
dc.identifier.issn
0041-6932
dc.identifier.uri
http://hdl.handle.net/11336/55216
dc.description.abstract
An asteroidal triple is a stable set of three vertices such that each pair is connected by a path avoiding the neighborhood of the third vertex. An asteroidal quadruple is a stable set of four vertices such that any three of them is an asteroidal triple. Two non adjacent vertices are linked by a special connection if either they have a common neighbor or they are the endpoints of two vertex-disjoint chordless paths satisfying certain technical conditions. Cameron, Ho`ang, and L´evˆeque [DIMAP Workshop on Algorithmic Graph Theory, 67–74, Electron. Notes Discrete Math., 32, Elsevier, 2009] proved that if a pair of non adjacent vertices are linked by a special connection then in any directed path model T the subpaths of T corresponding to the vertices forming the special connection have to overlap and they force T to be completely directed in one direction between these vertices. Special connections along with the concept of asteroidal quadruple play an important role to study rooted directed path graphs, which are the intersection graphs of directed paths in a rooted directed tree. In this work we define other special connections; these special connections along with the ones defined by Cameron, Ho`ang, and L´evˆeque are nine in total, and we prove that every one forces T to be completely directed in one direction between these vertices. Also, we give a characterization of rooted directed path graphs whose rooted models cannot be rooted on a bold maximal clique. As a by-product of our result, we build new forbidden induced subgraphs for rooted directed path graphs.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Unión Matemática Argentina
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dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Path
dc.subject
Asteroidals
dc.subject.classification
Matemática Pura
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
On rooted directed path graphs
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-08-08T14:58:58Z
dc.identifier.eissn
1669-9637
dc.journal.volume
57
dc.journal.number
1
dc.journal.pagination
114-144
dc.journal.pais
Argentina
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dc.journal.ciudad
Bahía Blanca
dc.description.fil
Fil: Tondato, Silvia Beatriz. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
dc.description.fil
Fil: Gutierrez, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
dc.journal.title
Revista de la Unión Matemática Argentina
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/pdf/v57n1/v57n1a09.pdf
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/revuma.php?p=toc/vol57
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