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Homomorphism duality pairs play a crucial role in the theory of relational structures and in the Constraint Satisfaction Problem. The case where both classes are finite is fully characterized. The case when both side are infinite seems to be very complex. It is also known that no finite-infinite duality pair is possible if we make the additional restriction… (More)

We present an O(n log log n+2)-time algorithm for nding n disjoint monochro-matic edges in a complete geometric graph of 3n ? 1 vertices, where the edges are colored by two colors. A geometric graph is a graph drawn in the plane so that every vertex corresponds to a point, and every edge is a closed straight-line segment connecting two vertices but not… (More)

A new, constructive proof with a small explicit constant is given to the Erd˝ os-Pyber theorem which says that the edges of a graph on n vertices can be partitioned into complete bipartite subgraphs so that every vertex is covered at most O(n/ log n) times. The theorem is generalized to uniform hypergraphs. Similar bounds with smaller constant value is… (More)

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