The 6-girth-thickness of the complete graph

Héctor Castañeda-López; Pablo C. Palomino; Andrea B. Ramos-Tort; Christian Rubio-Montiel; Claudia Silva-Ruíz

doi:10.1016/j.akcej.2019.05.004

The 6-girth-thickness of the complete graph

Combinatorics 2022-01-21 v4

Authors: Héctor Castañeda-López , Pablo C. Palomino , Andrea B. Ramos-Tort , Christian Rubio-Montiel , Claudia Silva-Ruíz

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Abstract

The $g$ -girth-thickness $\theta(g,G)$ of a graph $G$ is the minimum number of planar subgraphs of girth at least $g$ whose union is $G$ . In this paper, we determine the $6$ -girth-thickness $\theta(6,K_n)$ of the complete graph $K_n$ in almost all cases. And also, we calculate by computer the missing value of $\theta(4,K_n)$ .

Keywords

girth-thickness complete graph planar subgraphs graph thickness

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@article{arxiv.1709.07466,
  title  = {The 6-girth-thickness of the complete graph},
  author = {Héctor Castañeda-López and Pablo C. Palomino and Andrea B. Ramos-Tort and Christian Rubio-Montiel and Claudia Silva-Ruíz},
  journal= {arXiv preprint arXiv:1709.07466},
  year   = {2022}
}

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10 pages, 8 figures

The 6-girth-thickness of the complete graph

Abstract

Keywords

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