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5 papers · 2 filters
Combinatorial Alexander Duality -- a Short and Elementary Proof
Anders Björner, Martin Tancer
Let X be a simplicial complex with the ground set V. Define its Alexander dual as a simplicial complex X* = {A \subset V: V \setminus A \notin X}. The combinatorial Alexander duali…
Towards the Distribution of the Size of a Largest Planar Matching and Largest Planar Subgraph in Random Bipartite Graphs
Marcos Kiwi, Martin Loebl
We address the following question: When a randomly chosen regular bipartite multi--graph is drawn in the plane in the ``standard way'', what is the distribution of its maximum size…
Latin bitrades derived from groups
Nicholas J. Cavenagh, Ales Drapal, Carlo Hamalainen
A latin bitrade is a pair of partial latin squares which are disjoint, occupy the same set of non-empty cells, and whose corresponding rows and columns contain the same set of entr…
Graph coloring with no large monochromatic components
N. Linial, J. Matousek, O. Sheffet +1
For a graph G and an integer t we let mcc_t(G) be the smallest m such that there exists a coloring of the vertices of G by t colors with no monochromatic connected subgraph having…
Monochromatic triangles in two-colored plane
Vit Jelinek, Jan Kyncl, Rudolf Stolar +1
We prove that for any partition of the plane into a closed set and an open set and for any configuration of three points, there is a translated and rotated copy of …