![]() | THE ELECTRONIC JOURNAL OF COMBINATORICS (ed. March 2001), DS #5. |
1 By C(n,k) we denote the binomial
coefficient n!/(k!(n-k)!).
2 Two figures in the plane are congruent if one
can be transformed into the other by rotations and translations in
the plane.
3 A graph is three-connected if the removal of
any two vertices (and the adjacent edges) leaves a connected graph.
4 The prism of a graph G is formed by taking
two copies of G and adding a perfect matching whose edges join
corresponding copies of vertices.
5 A planar graph is one that can be embedded in the plane
without crossing edges. A plane graph is a planar graph that has
been embedded in the plane.
6 The square of a graph G,
denoted G2,
is the graph obtained from G by adding edges between vertices if
they are at distance 2 in G.
All of the original edges of G are present in
G2.
7 A link is a finite collection of
non-intersecting knots.
A Brunnian link is a link which is non-trivial,
yet every proper sub-collection is trivial.
A trivial link is one that can be projected to a collection of
non-intersecting circles in the plane.
![]() | THE ELECTRONIC JOURNAL OF COMBINATORICS (ed. March 2001), DS #5. |