Out-degree reducing partitions of digraphs

@article{BangJensen2017OutdegreeRP,
  title={Out-degree reducing partitions of digraphs},
  author={J{\o}rgen Bang-Jensen and St{\'e}phane Bessy and Fr{\'e}d{\'e}ric Havet and Anders Yeo},
  journal={ArXiv},
  year={2017},
  volume={abs/1707.09349}
}

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References

SHOWING 1-10 OF 15 REFERENCES

Finding good 2-partitions of digraphs II. Enumerable properties

PERMANENTS, PFAFFIAN ORIENTATIONS, AND EVEN DIRECTED CIRCUITS

A structural characterization of the feasible instances is proved, which implies a polynomial-time algorithm to solve all of the above problems.

Digraphs - theory, algorithms and applications

Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science, and it will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

The complexity of satisfiability problems

An infinite class of satisfiability problems is considered which contains these two particular problems as special cases, and it is shown that every member of this class is either polynomial-time decidable or NP-complete.

The even cycle problem for directed graphs

If each arc in a strongly connected directed graph of minimum in- degree and outdegree at least 3 is assigned a weight 0 or 1, then the resulting weighted directed graph has a directed cycle of even

Majority Colourings of Digraphs

We prove that every digraph has a vertex 4-colouring such that for each vertex $v$, at most half the out-neighbours of $v$ receive the same colour as $v$. We then obtain several results related to

Splitting digraphs

  • N. Alon
  • Mathematics
    Combinatorics, Probability and Computing
  • 2006
There are several known results asserting that undirected graphs can be partitioned in a way that satisfies various constraints imposed on the degrees, and three problems of this type are listed.

Some Connections Between Set Theory and Computer Science

  • R. Cowen
  • Mathematics
    Kurt Gödel Colloquium
  • 1993
Methods originating in theoretical computer science for showing that certain decision problems are NP-complete have also been used to show that certain compactness theorems are equivalent in ZF set

ON THE TWO-COLOURING OF HYPERGRAPHS

Finding good 2-partitions of digraphs I. Hereditary properties