Pebbling in Split Graphs
- Autores
- Alcón, Liliana Graciela; Gutierrez, Marisa; Hurlbert, Glenn
- Año de publicación
- 2014
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Graph pebbling is a network optimization model for transporting discrete resourcesthat are consumed in transit: the movement of 2 pebbles across an edge consumes one of thepebbles. The pebbling number of a graph is the fewest number of pebblestso that, from anyinitial configuration oftpebbles on its vertices, one can place a pebble on any given target vertex viasuch pebbling steps. It is known that deciding whether a given configuration on a particular graphcan reach a specified target isNP-complete, even for diameter 2 graphs, and that deciding whetherthe pebbling number has a prescribed upper bound is ΠP2-complete. On the other hand, for manyfamilies of graphs there are formulas or polynomial algorithms for computing pebbling numbers; forexample, complete graphs, products of paths (including cubes), trees, cycles, diameter 2 graphs, andmore. Moreover, graphs having minimum pebbling number are called Class 0, and many authors havestudied which graphs are Class 0 and what graph properties guarantee it, with no characterizationin sight. In this paper we investigate an important family of diameter 3 chordal graphs called splitgraphs; graphs whose vertex set can be partitioned into a clique and an independent set. We provide aformula for the pebbling number of a split graph, along with an algorithm for calculating it that runsinO(nβ) time, whereβ=2ω/(ω+1)∼=1.41 andω∼=2.376 is the exponent of matrix multiplication.Furthermore we determine that all split graphs with minimum degree at least 3 are Class 0.
Fil: Alcón, Liliana Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Gutierrez, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Hurlbert, Glenn. Arizona State University; Estados Unidos - Materia
-
Pebbling Number
Split Graphs
Class 0
Graph Algorithms
Complexity - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/32989
Ver los metadatos del registro completo
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Pebbling in Split GraphsAlcón, Liliana GracielaGutierrez, MarisaHurlbert, GlennPebbling NumberSplit GraphsClass 0Graph AlgorithmsComplexityhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Graph pebbling is a network optimization model for transporting discrete resourcesthat are consumed in transit: the movement of 2 pebbles across an edge consumes one of thepebbles. The pebbling number of a graph is the fewest number of pebblestso that, from anyinitial configuration oftpebbles on its vertices, one can place a pebble on any given target vertex viasuch pebbling steps. It is known that deciding whether a given configuration on a particular graphcan reach a specified target isNP-complete, even for diameter 2 graphs, and that deciding whetherthe pebbling number has a prescribed upper bound is ΠP2-complete. On the other hand, for manyfamilies of graphs there are formulas or polynomial algorithms for computing pebbling numbers; forexample, complete graphs, products of paths (including cubes), trees, cycles, diameter 2 graphs, andmore. Moreover, graphs having minimum pebbling number are called Class 0, and many authors havestudied which graphs are Class 0 and what graph properties guarantee it, with no characterizationin sight. In this paper we investigate an important family of diameter 3 chordal graphs called splitgraphs; graphs whose vertex set can be partitioned into a clique and an independent set. We provide aformula for the pebbling number of a split graph, along with an algorithm for calculating it that runsinO(nβ) time, whereβ=2ω/(ω+1)∼=1.41 andω∼=2.376 is the exponent of matrix multiplication.Furthermore we determine that all split graphs with minimum degree at least 3 are Class 0.Fil: Alcón, Liliana Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Gutierrez, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Hurlbert, Glenn. Arizona State University; Estados UnidosSociety for Industrial and Applied Mathematics2014-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/32989Hurlbert, Glenn; Gutierrez, Marisa; Alcón, Liliana Graciela; Pebbling in Split Graphs; Society for Industrial and Applied Mathematics; Siam Journal On Discrete Mathematics; 28; 3; 8-2014; 1449-14660895-4801CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1137/130914607info:eu-repo/semantics/altIdentifier/url/http://epubs.siam.org/doi/10.1137/130914607info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:32:22Zoai:ri.conicet.gov.ar:11336/32989instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:32:22.372CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
Pebbling in Split Graphs |
| title |
Pebbling in Split Graphs |
| spellingShingle |
Pebbling in Split Graphs Alcón, Liliana Graciela Pebbling Number Split Graphs Class 0 Graph Algorithms Complexity |
| title_short |
Pebbling in Split Graphs |
| title_full |
Pebbling in Split Graphs |
| title_fullStr |
Pebbling in Split Graphs |
| title_full_unstemmed |
Pebbling in Split Graphs |
| title_sort |
Pebbling in Split Graphs |
| dc.creator.none.fl_str_mv |
Alcón, Liliana Graciela Gutierrez, Marisa Hurlbert, Glenn |
| author |
Alcón, Liliana Graciela |
| author_facet |
Alcón, Liliana Graciela Gutierrez, Marisa Hurlbert, Glenn |
| author_role |
author |
| author2 |
Gutierrez, Marisa Hurlbert, Glenn |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
Pebbling Number Split Graphs Class 0 Graph Algorithms Complexity |
| topic |
Pebbling Number Split Graphs Class 0 Graph Algorithms Complexity |
| purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| dc.description.none.fl_txt_mv |
Graph pebbling is a network optimization model for transporting discrete resourcesthat are consumed in transit: the movement of 2 pebbles across an edge consumes one of thepebbles. The pebbling number of a graph is the fewest number of pebblestso that, from anyinitial configuration oftpebbles on its vertices, one can place a pebble on any given target vertex viasuch pebbling steps. It is known that deciding whether a given configuration on a particular graphcan reach a specified target isNP-complete, even for diameter 2 graphs, and that deciding whetherthe pebbling number has a prescribed upper bound is ΠP2-complete. On the other hand, for manyfamilies of graphs there are formulas or polynomial algorithms for computing pebbling numbers; forexample, complete graphs, products of paths (including cubes), trees, cycles, diameter 2 graphs, andmore. Moreover, graphs having minimum pebbling number are called Class 0, and many authors havestudied which graphs are Class 0 and what graph properties guarantee it, with no characterizationin sight. In this paper we investigate an important family of diameter 3 chordal graphs called splitgraphs; graphs whose vertex set can be partitioned into a clique and an independent set. We provide aformula for the pebbling number of a split graph, along with an algorithm for calculating it that runsinO(nβ) time, whereβ=2ω/(ω+1)∼=1.41 andω∼=2.376 is the exponent of matrix multiplication.Furthermore we determine that all split graphs with minimum degree at least 3 are Class 0. Fil: Alcón, Liliana Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina Fil: Gutierrez, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina Fil: Hurlbert, Glenn. Arizona State University; Estados Unidos |
| description |
Graph pebbling is a network optimization model for transporting discrete resourcesthat are consumed in transit: the movement of 2 pebbles across an edge consumes one of thepebbles. The pebbling number of a graph is the fewest number of pebblestso that, from anyinitial configuration oftpebbles on its vertices, one can place a pebble on any given target vertex viasuch pebbling steps. It is known that deciding whether a given configuration on a particular graphcan reach a specified target isNP-complete, even for diameter 2 graphs, and that deciding whetherthe pebbling number has a prescribed upper bound is ΠP2-complete. On the other hand, for manyfamilies of graphs there are formulas or polynomial algorithms for computing pebbling numbers; forexample, complete graphs, products of paths (including cubes), trees, cycles, diameter 2 graphs, andmore. Moreover, graphs having minimum pebbling number are called Class 0, and many authors havestudied which graphs are Class 0 and what graph properties guarantee it, with no characterizationin sight. In this paper we investigate an important family of diameter 3 chordal graphs called splitgraphs; graphs whose vertex set can be partitioned into a clique and an independent set. We provide aformula for the pebbling number of a split graph, along with an algorithm for calculating it that runsinO(nβ) time, whereβ=2ω/(ω+1)∼=1.41 andω∼=2.376 is the exponent of matrix multiplication.Furthermore we determine that all split graphs with minimum degree at least 3 are Class 0. |
| publishDate |
2014 |
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2014-08 |
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http://hdl.handle.net/11336/32989 Hurlbert, Glenn; Gutierrez, Marisa; Alcón, Liliana Graciela; Pebbling in Split Graphs; Society for Industrial and Applied Mathematics; Siam Journal On Discrete Mathematics; 28; 3; 8-2014; 1449-1466 0895-4801 CONICET Digital CONICET |
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Hurlbert, Glenn; Gutierrez, Marisa; Alcón, Liliana Graciela; Pebbling in Split Graphs; Society for Industrial and Applied Mathematics; Siam Journal On Discrete Mathematics; 28; 3; 8-2014; 1449-1466 0895-4801 CONICET Digital CONICET |
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