Out-degree reducing partitions of digraphs

  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},

Majority Colorings of Sparse Digraphs

A fractional relaxation of majority coloring proposed by Kreutzer et al. is dealt with and it is shown that every digraph has a fractional majority 3.9602-coloring.

Bipartite spanning sub(di)graphs induced by 2‐partitions

It is proved that it is polynomially solvable to decide whether a digraph $D$ has a 2-partition such that each vertex in $V_1$ has an out-neighbour in £V_2 and each vertices in V_2 has an in-neIGHbour in $\cal NP$, and even if the input is a highly connected eulerian digraph.

Classes of intersection digraphs with good algorithmic properties

It is proved that various classes of reflexive intersection digraphs have bounded bi-mimwidth and a novel framework of directed versions of locally checkable problems, that streamlines the definitions and the study of many problems in the literature and facilitates their common algorithmic treatment.

Out‐colourings of digraphs

It is proved that there exists an absolute positive constant $c$ so that every semicomplete digraph of minimum out-degree at least $2k+c\sqrt{k}$ has such a partition, tight up to the value of $c$.

Low chromatic spanning sub(di)graphs with prescribed degree or connectivity properties

Generalizing well‐known results of Erdős and Lovász, we show that every graph G contains a spanning k ‐partite subgraph H with λ ( H ) ≥ k − 1 k λ ( G ) , where λ ( G ) is the edge‐connectivity of G



Finding good 2-partitions of digraphs II. Enumerable properties


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


Finding good 2-partitions of digraphs I. Hereditary properties