Serge C. Ballif

collaborators

2 papers

math.CO2011

Upper Bounds on Sets of Orthogonal Colorings of Graphs

Serge C. Ballif

We generalize the notion of orthogonal latin squares to colorings of simple graphs. Two $n$ -colorings of a graph are said to be \emph{orthogonal} if whenever two vertices share a c…

math.CO2011

Conditions to Extend Partial Latin Rectangles

Serge C. Ballif

In 1974 Allan Cruse provided necessary and sufficient conditions to extend an $r \times s$ partial latin rectangle consisting of $t$ distinct symbols to a latin square of order $n$ .…