CENTROID OF A QUADRANGLE

Bedrock Geology of Herod Quadrangle

Hexagon quadrangle systems

A hexagon quadrangle system of order n and index [HQS (n)] is a pair (X,H), where X is a finite set of n vertices and H is a collection of edge disjoint hexagon quadrangles (called blocks) which partitions the edge set of Kn, with vertex set X. A hexagon quadrangle system is said to be a 4-nesting [N(4) − HQS] if the collection of all the 4-cycles contained in the hexagon quadrangles is a /2-fo...

Perfect dodecagon quadrangle systems

A dodecagon quadrangle is the graph consisting of two cycles: a 12-cycle (x1, x2, ..., x12) and a 4-cycle (x1, x4, x7, x10). A dodecagon quadrangle system of order n and index ρ [DQS] is a pair (X, H), where X is a finite set of n vertices and H is a collection of edge disjoint dodecagon quadrangles (called blocks) which partitions the edge set of ρKn, with vertex set X. A dodecagon quadrangle ...

Shrinkage simplex-centroid designs for a quadratic mixture model

A simplex-centroid design for q mixture components comprises of all possible subsets of the q components, present in equal proportions. The design does not contain full mixture blends except the overall centroid. In real-life situations, all mixture blends comprise of at least a minimum proportion of each component. Here, we introduce simplex-centroid designs which contain complete blend...

Decompositions of quadrangle-free planar graphs

W. He et al. showed that a planar graph not containing 4-cycles can be decomposed into a forest and a graph with maximum degree at most 7. This degree restriction was improved to 6 by Borodin et al. We further lower this bound to 5 and show that it cannot be improved to 3.