DM
2010
13 years 11 months ago
2010
Using a generalisation of Hamiltonian cycles to uniform hypergraphs due to Katona and Kierstead, we define a new notion of a Hamiltonian decomposition of a uniform hypergraph. We ...
DM
2010
13 years 11 months ago
2010
In this paper, we first prove some general results on the number of fixed points of collineations of finite partial geometries, and on the number of absolute points of dualities o...
DM
2010
13 years 11 months ago
2010
Let Mad(G) denote the maximum average degree (over all subgraphs) of G and let i(G) denote the injective chromatic number of G. We prove that if Mad(G) 5 2 , then i(G) + 1; sim...
DM
2010
13 years 11 months ago
2010
DM
2010
13 years 11 months ago
2010
This paper solves the Knights and Spies Problem: In a room there are n people, each labelled with a unique number between 1 and n. A person may either be a knight or a spy. Knights...
DM
2010
13 years 11 months ago
2010
Given a polygon P in the plane, a pop operation is the reflection of a vertex with respect to the line through its adjacent vertices. We define a family of alternating polygons, a...
DM
2010
13 years 11 months ago
2010
DM
2010
13 years 11 months ago
2010
Let H 2V be a hypergraph on vertex set V . For a positive integer r, we call H r-exact, if any minimal transversal of H intersects any hyperedge of H in at most r vertices. This ...
DM
2010
13 years 11 months ago
2010
DM
2010
13 years 11 months ago
2010
For a non-negative integer T, we prove that the independence number of a graph G = (V, E) in which every vertex belongs to at most T triangles is at least uV f(d(u), T) where d(u)...