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On cylindrical graph construction and its applications

Daneshgar, A ; Sharif University of Technology | 2016

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  1. Type of Document: Article
  2. Publisher: Australian National University , 2016
  3. Abstract:
  4. In this article we introduce the cylindrical construction, as an edge-replacement procedure admitting twists on both ends of the hyperedges, generalizing the concepts of lifts and Pultr templates at the same time. We prove a tensor-hom duality for this construction and we show that not only a large number of well-known graph constructions are cylindrical but also the construction and its dual give rise to some new graph constructions, applications and results. To show the applicability of the main duality we introduce generalized Grötzsch, generalized Petersen-like and Coxeter-like graphs and we prove some coloring properties of these graphs
  5. Keywords:
  6. Adjoint functor ; Category of graphs ; Coxeter-like graphs ; Cylindrical construction ; Extremal problems ; Generalized mycielski construction ; Generalized petersen graph ; Graph homomorphism ; Labeled and marked graphs
  7. Source: Electronic Journal of Combinatorics ; Volume 23, Issue 1 , 2016 ; 10778926 (ISSN)
  8. URL: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i1p29