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COMBINATORICA
2010
13 years 22 days ago
2010
We show that the topological cycle space of a locally finite graph is a canonical quotient of the first singular homology group of its Freudenthal compactification, and we charact...
COMBINATORICA
2010
13 years 3 months ago
2010
A d-dimensional polycube is a facet-connected set of cubes in d dimensions. Fixed polycubes are considered distinct if they differ in their shape or orientation. A proper d-dimens...
COMBINATORICA
2010
13 years 3 months ago
2010
Consider the following one-player game. The vertices of a random graph on n vertices are revealed to the player one by one. In each step, also all edges connecting the newly reveal...
COMBINATORICA
2010
13 years 3 months ago
2010
In this paper, we propose a simple and natural randomized algorithm to embed a tree T in a given graph G. The algorithm can be viewed as a "self-avoiding tree-indexed random ...
COMBINATORICA
2010
13 years 22 days ago
2010
We prove that the edges of every graph of bounded (Euler) genus can be partitioned into any prescribed number k of pieces such that contracting any piece results in a graph of bou...