On treewidth and minimum fill-in of asteroidal triple-free graphs
Ordal'94 Selected papers from the conference on Orders, algorithms and applications
Characterizations and algorithmic applications of chordal graph embeddings
Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
A practical algorithm for making filled graphs minimal
Theoretical Computer Science
Treewidth and Minimum Fill-in: Grouping the Minimal Separators
SIAM Journal on Computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Computing Minimal Triangulations in Time O(n\alpha \log n) = o(n2.376)
SIAM Journal on Discrete Mathematics
A wide-range algorithm for minimal triangulation from an arbitrary ordering
Journal of Algorithms
Characterizing minimal interval completions towards better understanding of profile and pathwidth
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Strongly chordal and chordal bipartite graphs are sandwich monotone
Journal of Combinatorial Optimization
An O(n2)-time algorithm for the minimal interval completion problem
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Faster parameterized algorithms for deletion to split graphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
An O( n2)-time algorithm for the minimal interval completion problem
Theoretical Computer Science
| Hi-index | 0.05 |
We study the problem of adding an inclusion minimal set of edges to a given arbitrary graph so that the resulting graph is a split graph, called a minimal split completion of the input graph. Minimal completions of arbitrary graphs into chordal and interval graphs have been studied previously, and new results have been added recently. We extend these previous results to split graphs by giving a linear-time algorithm for computing minimal split completions. We also give two characterizations of minimal split completions, which lead to a linear time algorithm for extracting a minimal split completion from any given split completion. We prove new properties of split graph that are both useful for our algorithms and interesting on their own. First, we present a new way of partitioning the vertices of a split graph uniquely into three subsets. Second, we prove that split graphs have the following property: given two split graphs on the same vertex set where one is a subgraph of the other, there is a sequence of edges that can be removed from the larger to obtain the smaller such that after each edge removal the modified graph is split.