• Corpus ID: 16837970

Degree-constrained Subgraph Reconfiguration is in P

  title={Degree-constrained Subgraph Reconfiguration is in P},
  author={Moritz Muhlenthaler},
The degree-constrained subgraph problem asks for a subgraph of a given graph such that the degree of each vertex is within some specified bounds. We study the following reconfiguration variant of this problem: Given two solutions to a degree-constrained subgraph instance, can we transform one solution into the other by adding and removing individual edges, such that each intermediate subgraph satisfies the degree constraints and contains at least a certain minimum number of edges? This problem… 

Figures from this paper

Reconfiguring spanning and induced subgraphs
This paper systematically clarify the complexity status of subgraph reconfiguration with respect to graph structure properties.
No Title Given
Introduction to Reconfiguration
Reconfiguration is concerned with relationships among solutions to a problem instance, where the reconfiguration of one solution to another is a sequence of steps such that each step produces an
Reconfiguring Directed Trees in a Digraph
This paper focuses on the problem of determining whether, given two directed trees in a digraph, there is a (reconfiguration) sequence of directed trees such that for every pair of two consecutive trees in the sequence, one of them is obtained from the other by removing an arc and then adding another arc.
Shortest Reconfiguration of Perfect Matchings via Alternating Cycles
It is proved that the shortest reconfiguration problem of perfect matchings via alternating cycles is NP-hard even when a given graph is planar or bipartite, but it can be solved in polynomial time when the graph is outerplanar.
Reconfiguration of graph minors
The reconfiguration framework is considered, including a full characterization of graphs $G$ that result in connectivity for $K_2$-models, as well as the relationship between connectivity of G and other $H-models and other graphs.
Sliding Tokens on a Cactus
A polynomial-time algorithm for solving Sliding Token in case the graph G is a cactus is described and a no-instance may be easily deduced using this characterization.


An efficient reduction technique for degree-constrained subgraph and bidirected network flow problems
Efficient algorithms are given for the bidirected network flow problem and the degree-constrained subgraph problem, which use a reduction technique that solves one problem instance by reducing to a number of problems.
Another Look at the Degree Constrained Subgraph Problem
The Complexity of Rerouting Shortest Paths
For claw-free graphs and chordal graphs, it is shown that the Shortest Path Reconfiguration problem can be solved in polynomial time, and that shortest rerouting sequences have linear length.
On the complexity of reconfiguration problems
Finding paths between 3‐colorings
Given a 3‐colorable graph G together with two proper vertex 3‐colorings α and β of G, consider the following question: is it possible to transform α into β by recoloring vertices of G one at a time,
The complexity of change
Many combinatorial problems can be formulated as "Can I transform configuration 1 into configuration 2, if certain transformations only are allowed?". An example of such a question is: given two
Homomorphism reconfiguration via homotopy
The positive side of this dichotomy is generalized by providing an algorithm that solves the problem in polynomial time for any H with no C_4 subgraph, which gives a large class of constraints for which finding solutions to the Constraint Satisfaction Problem is NP-complete, but finding paths in the solution space is P.
Gabow . An efficient reduction technique for degree - constrained subgraph and bidirected network flow problems