• Corpus ID: 257405191

Efficient enumeration of maximal split subgraphs and induced sub-cographs and related classes

  title={Efficient enumeration of maximal split subgraphs and induced sub-cographs and related classes},
  author={Caroline Brosse and Aur{\'e}lie Lagoutte and Vincent Limouzy and Arnaud Mary and Lucas Pastor},
In this paper, we are interested in algorithms that take in input an arbitrary graph $G$, and that enumerate in output all the (inclusion-wise) maximal"subgraphs"of $G$ which fulfil a given property $\Pi$. All over this paper, we study several different properties $\Pi$, and the notion of subgraph under consideration (induced or not) will vary from a result to another. More precisely, we present efficient algorithms to list all maximal split subgraphs, sub-cographs and some subclasses of… 



Enumerating Maximal Induced Subgraphs

  • Yixin Cao
  • Mathematics, Computer Science
  • 2020
The $t$-restricted version of the maximal (connected) induced subgraphs problem is introduced, and it is equivalent to the original problem in terms of solvability in incremental polynomial time.

On the Enumeration of Minimal Dominating Sets and Related Notions

It is shown that there exists an output-polynomial time algorithm for the Dom-enum problem (or equivalently Trans-Enum problem) if and only if there exists one for the following enumeration problems: minimal total dominating sets, minimal total dominate sets in split graphs, minimal connected dominating sets insplit graphs, and minimal total dominated sets in co-bipartite graphs.

New polynomial delay bounds for maximal subgraph enumeration by proximity search

This paper proposes polynomial delay algorithms for several maximal subgraph listing problems, by means of a seemingly novel technique which is called proximity search, and presents these algorithms, and gives insight on how this general technique can be applied to other problems.

Faster and Enhanced Inclusion-Minimal Cograph Completion

It is proved that many very sparse graphs, having only O(n) edges, require \(\varOmega (n^2)\) edges in any of their cograph completions, and the complexity of inclusion-minimal completion is improved on the complexity scales as \(O(n/\log ^2 n)\).

Minimal split completions

On Maximal Chain Subgraphs and Covers of Bipartite Graphs

The problem of enumerating all minimal chain subgraph covers of a bipartite graph is approached and it is shown that it can be solved in quasi-polynomial time.

Edge-Deletion Problems

This paper shows that the edge-deletion problem is NP-complete for the following properties: (1) without cycles of specified length l, or of any length $ \leqq l$, (2) connected and degree-constrained, (3) outerplanar, (4) transitive digraph, (5) line-invertible, (6) bipartite, (7)transitively orientable.

Single-edge monotonic sequences of graphs and linear-time algorithms for minimal completions and deletions

A New Algorithm for Generating All the Maximal Independent Sets

This paper presents a new efficient algorithm for generating all the maximal independent sets, for which processing time and memory space are bounded by $O(nm\mu)$ and $O (n+m)$, respectively, where n, m, and $\mu$ are the numbers of vertices, edges, and maximalIndependent sets of a graph.

Generating all Maximal Independent Sets: NP-Hardness and Polynomial-Time Algorithms

It is shown that it is possible to apply ideas of Paull and Unger and of Tsukiyama et al. to obtain polynomial-time algorithms for a number of special cases, e.g. the efficient generation of all maximal feasible solutions to a knapsack problem.