Quadrangle groups inclusions

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 ...

Bedrock Geology of Herod Quadrangle

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.

Geology of the Victoria quadrangle (H02), Mercury

Mercury’s quadrangle H02 ‘Victoria’ is located in the planet’s northern hemisphere and lies between latitudes 22.5° N and 65° N, and between longitudes 270° E and 360° E. This quadrangle covers 6.5% of the planet’s surface with a total area of almost 5 million km. Our 1:3,000,000-scale geologic map of the quadrangle was produced by photo-interpretation of remotely sensed orbital images captured...