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Watkins snark | |
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The Watkins snark | |

Named after | J. J. Watkins |

Vertices | 50 |

Edges | 75 |

Radius | 7 |

Diameter | 7 |

Girth | 5 |

Automorphisms | 5 |

Chromatic number | 3 |

Chromatic index | 4 |

Book thickness | 3 |

Queue number | 2 |

Properties | Snark |

Table of graphs and parameters |

In the mathematical field of graph theory, the **Watkins snark** is a snark with 50 vertices and 75 edges.^{ [1] }^{ [2] } It was discovered by John J. Watkins in 1989.^{ [3] }

**Mathematics** includes the study of such topics as quantity, structure, space, and change.

In mathematics, **graph theory** is the study of *graphs*, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of *vertices* which are connected by *edges*. A distinction is made between **undirected graphs**, where edges link two vertices symmetrically, and **directed graphs**, where edges link two vertices asymmetrically; see Graph for more detailed definitions and for other variations in the types of graph that are commonly considered. Graphs are one of the prime objects of study in discrete mathematics.

In the mathematical field of graph theory, a **snark** is a simple, connected, bridgeless cubic graph with chromatic index equal to 4. In other words, it is a graph in which every vertex has three neighbors, the connectivity is redundant so that removing no one edge would split the graph, and the edges cannot be colored by only three colors without two edges of the same color meeting at a point. In order to avoid trivial cases, snarks are often restricted to have girth at least 5.

As a snark, the Watkins graph is a connected, bridgeless cubic graph with chromatic index equal to 4. The Watkins snark is also non-planar and non-hamiltonian. It has book thickness 3 and queue number 2.^{ [4] }

In graph theory, a **bridge**, **isthmus**, **cut-edge**, or **cut arc** is an edge of a graph whose deletion increases its number of connected components. Equivalently, an edge is a bridge if and only if it is not contained in any cycle. A graph is said to be **bridgeless** or **isthmus-free** if it contains no bridges.

In the mathematical field of graph theory, a **cubic graph** is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are also called **trivalent graphs**.

In graph theory, a **planar graph** is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a **plane graph** or **planar embedding of the graph**. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points.

Another well known snark on 50 vertices is the Szekeres snark, the fifth known snark, discovered by George Szekeres in 1973.^{ [5] }

In the mathematical field of graph theory, the **Szekeres snark** is a snark with 50 vertices and 75 edges. It was the fifth known snark, discovered by George Szekeres in 1973.

**George Szekeres** AM FAA was a Hungarian–Australian mathematician.

- The chromatic number of the Watkins snark is 3.
- The chromatic index of the Watkins snark is 4.

[[1,2], [1,4], [1,15], [2,3], [2,8], [3,6], [3,37], [4,6], [4,7], [5,10], [5,11], [5,22], [6,9], [7,8], [7,12], [8,9], [9,14], [10,13], [10,17], [11,16], [11,18], [12,14], [12,33], [13,15], [13,16], [14,20], [15,21], [16,19], [17,18], [17,19], [18,30], [19,21], [20,24], [20,26], [21,50], [22,23], [22,27], [23,24], [23,25], [24,29], [25,26], [25,28], [26,31], [27,28], [27,48], [28,29], [29,31], [30,32], [30,36], [31,36], [32,34], [32,35], [33,34], [33,40], [34,41], [35,38], [35,40], [36,38], [37,39], [37,42], [38,41], [39,44], [39,46], [40,46], [41,46], [42,43], [42,45], [43,44], [43,49], [44,47], [45,47], [45,48], [47,50], [48,49], [49,50]]

In the mathematical field of graph theory, the **double-star snark** is a snark with 30 vertices and 45 edges.

In the mathematical field of graph theory, the **Ljubljana graph** is an undirected bipartite graph with 112 vertices and 168 edges.

Statistics of Swedish football Division 3 in season 2011.

Statistics of Swedish football Division 3 in season 2009.

Statistics of Swedish football Division 3 in season 2008.

Statistics of Swedish football Division 3 in season 2007.

Statistics of Swedish football Division 3 in season 2006.

Statistics of Swedish football Division 3 in season 2003.

Statistics of Swedish football Division 3 in season 2002.

Statistics of Swedish football Division 3 in season 2001.

Statistics of Swedish football Division 3 in season 2000.

Statistics of Swedish football Division 3 in season 1999.

Statistics of Swedish football Division 3 in season 1998.

Statistics of Swedish football Division 3 in season 1994.

Statistics of Swedish football Division 3 in season 1993.

**1990 Soviet Lower Second League** was the second season of the Soviet Second League B since its reestablishing in 1990. As in the last season it was divided into 10 zones (groups).

**1989 Soviet Second League** was a Soviet competition in the Soviet Second League.

**1989 Soviet Second League** was a Soviet competition in the Soviet Second League.

- ↑ Weisstein, Eric W. "Watkins Snark".
*MathWorld*. - ↑ Watkins, J. J. and Wilson, R. J. "A Survey of Snarks." In Graph Theory, Combinatorics, and Applications (Ed. Y. Alavi, G. Chartrand, O. R. Oellermann, and A. J. Schwenk). New York: Wiley, pp. 1129-1144, 1991
- ↑ Watkins, J. J. "Snarks." Ann. New York Acad. Sci. 576, 606-622, 1989.
- ↑ Wolz, Jessica;
*Engineering Linear Layouts with SAT*. Master Thesis, University of Tübingen, 2018 - ↑ Szekeres, G. (1973). "Polyhedral decompositions of cubic graphs".
*Bull. Austral. Math. Soc*.**8**(03): 367–387. doi:10.1017/S0004972700042660.

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