Flower snark

Flower snark
The flower snarks J3, J5 and J7.
Vertices4n
Edges6n
Girth3 for n=3
5 for n=5
6 for n≥7
Chromatic number3
Chromatic index4
Book thickness3 for n=5
3 for n=7
Queue number2 for n=5
2 for n=7
PropertiesSnark for n≥5
NotationJn with n odd
Table of graphs and parameters
Flower snark J5
The flower snark J5.
Vertices20
Edges30
Girth5
Chromatic number3
Chromatic index4
PropertiesSnark
Hypohamiltonian
Table of graphs and parameters

In the mathematical field of graph theory, the flower snarks form an infinite family of snarks introduced by Rufus Isaacs in 1975.[1]

As snarks, the flower snarks are connected, bridgeless cubic graphs with chromatic index equal to 4. The flower snarks are non-planar and non-Hamiltonian. The flower snarks J5 and J7 have book thickness 3 and queue number 2.[2]

  1. ^ Isaacs, R. (1975). "Infinite Families of Nontrivial Trivalent Graphs Which Are Not Tait Colorable". Amer. Math. Monthly. 82: 221–239. doi:10.1080/00029890.1975.11993805. JSTOR 2319844.
  2. ^ Wolz, Jessica; Engineering Linear Layouts with SAT. Master Thesis, University of Tübingen, 2018