The notions of a forcing edge and the forcing number of a perfect matching first appeared in
a 1991 paper [15] by Harary, Klein and Zivkovic. The root of these concepts can be traced to …

On defining sets for projective planes - ScienceDirect Skip to main contentSkip to article
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An embedding of a graph in a surface gives rise to a combinatorial design whose blocks
correspond to the faces of the embedding. Particularly interesting graphs include complete …

A pair x, y of vertices in a nontrivial connected graph G is said to geodominate a vertex v of G
if either v∈{x, y} or v lies in an x–y geodesic of G. A set S of vertices of G is a geodominating …

A critical set in an $ n\times n $ Latin square is a minimal set of entries that uniquely
identifies it among all Latin squares of the same size. It is conjectured by Nelder in 1979 …

Given a graph G and a k-colouring c, a critical set S is a minimal set of vertices S for which
the restriction of c to S determines c completely. There are four parameters that relate to the …

Excluding induced subgraphs Page 108 Excluding induced subgraphs 1 Maria Chudnovsky and
Paul Seymour Abstract In this paper we survey some results concerning the structure and …

arXiv:math/0701018v2 [math.CO] 14 Mar 2009 Perfect dominating sets in the Cartesian products
of prime cycles. Page 1 arXiv:math/0701018v2 [math.CO] 14 Mar 2009 Perfect dominating sets …

Trades, as combinatorial objects, possess interesting combinatorial and algebraic properties
and play a considerable role in various areas of combinatorial designs. In this paper we …

If D is a partially filled‐in (0, 1)‐matrix with a unique completion to a (0, 1)‐matrix M (with
prescribed row and column sums), we say that D is a defining set for M. If the removal of any …