umu.sePublikasjoner
Endre søk
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Edge precoloring extension of hypercubes
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
(engelsk)Manuskript (preprint) (Annet vitenskapelig)
Abstract [en]

We consider the problem of extending partial edge colorings of hypercubes. In particular, we obtain an analogue of the positive solution to the famous Evans' conjecture on completing partial Latin squares by proving that every proper partial edge coloring of at most (d-1) edges of the d-dimensional hypercube Qd can be extended to a proper d-edge coloring of Qd. Additionally, we characterize which partial edge colorings of Qd with precisely d precolored edges are extendable to proper d-edge colorings of Qd.

HSV kategori
Forskningsprogram
matematik
Identifikatorer
URN: urn:nbn:se:umu:diva-147508OAI: oai:DiVA.org:umu-147508DiVA, id: diva2:1203756
Tilgjengelig fra: 2018-05-04 Laget: 2018-05-04 Sist oppdatert: 2019-04-29
Inngår i avhandling
1. On avoiding and completing edge colorings
Åpne denne publikasjonen i ny fane eller vindu >>On avoiding and completing edge colorings
2018 (engelsk)Licentiatavhandling, med artikler (Annet vitenskapelig)
Abstract [en]

These papers are all related to the problem of avoiding and completing an edge precoloring of a graph. In more detail, given a graph G and a partial proper edge precoloring φ of G and a list assignment L for every non-colored edge of G, can we extend the precoloring to a proper edge coloring avoiding any list assignment? In the first paper, G is a d-dimensional hypercube graph Qd, a partial proper edge precoloring φ and every list assignment L must satisfy certain sparsity conditions. The second paper still deals with d-dimensional hypercube graph Qd, but the list assignment L for every edge of Qd is an empty set and φ must be a partial proper edge precoloring of at most (d - 1) edges. For the third paper, G can be seen as a complete 3-uniform 3-partite hypergraph, every list assignment L must satisfy certain sparsity conditions but we do not have a partial proper edge precoloring φ on edges of G. 

sted, utgiver, år, opplag, sider
Umeå: Umeå University, 2018. s. 8
Serie
Research report in mathematics, ISSN 1653-0810
HSV kategori
Forskningsprogram
matematik
Identifikatorer
urn:nbn:se:umu:diva-146915 (URN)978-91-7601-876-7 (ISBN)
Presentation
2018-05-17, MA346, MIT Building, Umea University, Umea, 13:00 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2018-05-25 Laget: 2018-05-04 Sist oppdatert: 2018-06-09bibliografisk kontrollert
2. On avoiding and completing colorings
Åpne denne publikasjonen i ny fane eller vindu >>On avoiding and completing colorings
2019 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

All of my papers are related to the problem of avoiding and completing an edge precoloring of a graph. In more detail, given a graph G and a partial proper edge precoloring φ of G and a list assignment L for every non-colored edge of G, can we extend φ to a proper edge coloring of G which avoids L? 

In Paper I, G is the d-dimensional hypercube graph Qd, a partial proper edge precoloring φ and a list assignment L must satisfy certain sparsity conditions. Paper II still deals with the hypercube graph Qd, but the list assignment L for every edge of Qd is an empty set and φ must be a partial proper edge precoloring of at most d-1 edges. In Paper III, G is a (d,s)-edge colorable graph; that is G has a proper d-edge coloring, where every edge is contained in at least s-1 2-colored 4-cycles, L must satisfy certain sparsity conditions and we do not have a partial proper edge precoloring φ on edges of G. The problem in Paper III is also considered in Paper IV and Paper V, but here G can be seen as the complete 3-uniform 3-partite hypergraph K3n,n,n, where n is a power of two in paper IV and n is an even number in paper V.

sted, utgiver, år, opplag, sider
Umeå: Umeå University, 2019. s. 11
Serie
Research report in mathematics, ISSN 1653-0810 ; 66/19
Emneord
Graph coloring, precoloring, list assignment
HSV kategori
Identifikatorer
urn:nbn:se:umu:diva-158343 (URN)978-91-7855-055-5 (ISBN)
Disputas
2019-05-24, MA121, MIT-huset, Umeå, 10:15 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2019-05-03 Laget: 2019-04-24 Sist oppdatert: 2019-04-29bibliografisk kontrollert

Open Access i DiVA

Fulltekst mangler i DiVA

Andre lenker

URL

Personposter BETA

Markström, KlasPham, Lan Anh

Søk i DiVA

Av forfatter/redaktør
Markström, KlasPham, Lan Anh
Av organisasjonen

Søk utenfor DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric

urn-nbn
Totalt: 83 treff
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf