Orthogonal art galleries with holes: a coloring proof of Aggarwal's theorem.
Orthogonal colorings of graphs.
Orthogonal designs II.
Orthogonal double covers of complete graphs by fat caterpillars
An orthogonal double cover (ODC) of the complete graph Kₙ by some graph G is a collection of n spanning subgraphs of Kₙ, all isomorphic to G, such that any two of the subgraphs share exactly one edge and every edge of Kₙ is contained in exactly two of the subgraphs. A necessary condition for such an ODC to exist is that G has exactly n-1 edges. We show that for any given positive integer d, almost all caterpillars of diameter d admit an ODC of the corresponding complete graph.
Orthogonal drawings of plane graphs without bends.
Orthogonal packings in PG(5, 2).
Orthogonal partitions
Orthogonal partitions and covering of graphs
Orthogonal permutation arrays and related structures
Orthogonal polynomials associated with root systems.
Orthogonal Resolutions and Latin Squares
Resolutions which are orthogonal to at least one other resolution (RORs) and sets of m mutually orthogonal resolutions (m-MORs) of 2-(v, k, λ) designs are considered. A dependence of the number of nonisomorphic RORs and m-MORs of multiple designs on the number of inequivalent sets of v/k − 1 mutually orthogonal latin squares (MOLS) of size m is obtained. ACM Computing Classification System (1998): G.2.1.∗ This work was partially supported by the Bulgarian National Science Fund under Contract No...
Orthogonal Steiner Systems.
Orthogonal systems.
Orthogonal systems in vector spaces over finite fields.
Orthogonal systems of n-ary operations and codes
Orthogonal vector coloring.
Osculating paths and oscillating tableaux.
Outerplanar crossing numbers, the circular arrangement problem and isoperimetric functions.
Ovals and non-ovoidal Laguerre planes.
Overlapping latin subsquares and full products
We derive necessary and sufficient conditions for there to exist a latin square of order containing two subsquares of order and that intersect in a subsquare of order . We also solve the case of two disjoint subsquares. We use these results to show that: (a) A latin square of order cannot have more than subsquares of order , where . Indeed, the number of subsquares of order is bounded by a polynomial of degree at most in . (b) For all there exists a loop of order in which every...