Discrete Applied Mathematics, ISSN 0166-218X, 08/2018, Volume 245, pp. 168 - 176

We study those unit interval graphs having a model with intervals of integer endpoints and prescribed length. We present a structural result for this graph...

Unit interval graphs | Forbidden induced subgraphs | Proper interval graphs | MATHEMATICS, APPLIED | Analysis | Algorithms

Unit interval graphs | Forbidden induced subgraphs | Proper interval graphs | MATHEMATICS, APPLIED | Analysis | Algorithms

Journal Article

Discrete Mathematics, ISSN 0012-365X, 11/2015, Volume 338, Issue 11, pp. 1907 - 1916

A perfect graph is a graph every subgraph of which has a chromatic number equal to its clique number (Berge, 1963; Lovász, 1972). A (vertex) weighted graph is...

Superperfect graphs | Unit interval graphs | Proper interval graphs | MATHEMATICS | Algorithms

Superperfect graphs | Unit interval graphs | Proper interval graphs | MATHEMATICS | Algorithms

Journal Article

European Journal of Operational Research, ISSN 0377-2217, 09/2013, Volume 229, Issue 2, pp. 332 - 344

•A new fast optimal split for the team orienteering problem.•An effective particle swarm algorithm (PSOiA).•PSOiA is robust and outperforms the...

Interval graph | Swarm intelligence | Vehicle routing | Optimal split | Knapsack problem | Vehicle routing Knapsack problem Interval graph Optimal split Swarm intelligence | PARTICLE SWARM OPTIMIZATION | 1ST | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SOLVE | Mathematical optimization | Analysis | Orienteering | Computer Science | Operations Research

Interval graph | Swarm intelligence | Vehicle routing | Optimal split | Knapsack problem | Vehicle routing Knapsack problem Interval graph Optimal split Swarm intelligence | PARTICLE SWARM OPTIMIZATION | 1ST | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SOLVE | Mathematical optimization | Analysis | Orienteering | Computer Science | Operations Research

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 05/2019, Volume 261, pp. 78 - 92

Graphs with bounded thinness were defined in 2007 as a generalization of interval graphs. In this paper we introduce the concept of proper thinness, such that...

Interval graphs | Proper thinness | Thinness | Proper interval graphs | MINORS | MATHEMATICS, APPLIED | NUMBER | BOUNDS | COMPLEXITY | DOMINATION | ALGORITHMS | Graphs | Polynomials

Interval graphs | Proper thinness | Thinness | Proper interval graphs | MINORS | MATHEMATICS, APPLIED | NUMBER | BOUNDS | COMPLEXITY | DOMINATION | ALGORITHMS | Graphs | Polynomials

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 08/2015, Volume 79, Issue 4, pp. 267 - 281

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 05/2017, Volume 222, pp. 151 - 165

Robinsonian matrices arise in the classical seriation problem and play an important role in many applications where unsorted similarity (or dissimilarity)...

Unit interval graph | Lex-BFS | Seriation | Straight enumeration | Robinson (dis)similarity | Partition refinement | PROPER INTERVAL-GRAPHS | MATHEMATICS, APPLIED | Algorithms

Unit interval graph | Lex-BFS | Seriation | Straight enumeration | Robinson (dis)similarity | Partition refinement | PROPER INTERVAL-GRAPHS | MATHEMATICS, APPLIED | Algorithms

Journal Article

Journal of Complex Networks, ISSN 2051-1310, 2016, Volume 4, Issue 2, pp. 224 - 244

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 11/2015, Volume 195, pp. 2 - 7

We introduce the non-unit count of an interval graph as the minimum number of intervals in an interval representation whose lengths deviate from one. We...

Interval graph | Unit interval graph | Comparability invariant | Intersection graph | MATHEMATICS, APPLIED | UNIT | PROPER

Interval graph | Unit interval graph | Comparability invariant | Intersection graph | MATHEMATICS, APPLIED | UNIT | PROPER

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 04/2015, Volume 576, Issue 1, pp. 85 - 101

Chordal graphs are intersection graphs of subtrees of a tree T. We investigate the complexity of the partial representation extension problem for chordal...

Interval graph | Chordal graph | Restricted representation | Intersection representation | Partial representation extension | INTERVAL-GRAPHS | RECOGNITION | COMPUTER SCIENCE, THEORY & METHODS | ALGORITHMS | Trees | Intervals | Subdivisions | Equivalence | Graphs | Representations | Topology | Complexity

Interval graph | Chordal graph | Restricted representation | Intersection representation | Partial representation extension | INTERVAL-GRAPHS | RECOGNITION | COMPUTER SCIENCE, THEORY & METHODS | ALGORITHMS | Trees | Intervals | Subdivisions | Equivalence | Graphs | Representations | Topology | Complexity

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 01/2017, Volume 216, pp. 67 - 83

A normal Helly circular-arc graph is the intersection graph of a set of arcs on a circle of which no three or less arcs cover the whole circle. Lin et al....

Holes | Linear-time | (proper) interval graphs | (minimal) forbidden induced subgraphs | Chordal graphs | (normal, Helly, proper) circular-arc models | Certifying algorithms | INTERVAL-GRAPHS | MATHEMATICS, APPLIED | RECOGNITION | SUBCLASSES | ALGORITHMS | Algorithms

Holes | Linear-time | (proper) interval graphs | (minimal) forbidden induced subgraphs | Chordal graphs | (normal, Helly, proper) circular-arc models | Certifying algorithms | INTERVAL-GRAPHS | MATHEMATICS, APPLIED | RECOGNITION | SUBCLASSES | ALGORITHMS | Algorithms

Journal Article

SIAM Journal on Computing, ISSN 0097-5397, 2011, Volume 40, Issue 5, pp. 1292 - 1315

We present a logspace algorithm for computing a canonical labeling, in fact, a canonical interval representation, for interval graphs. To achieve this, we...

Interval graphs | Convex graphs | Graph isomorphism | Logspace | Proper interval graphs | Graph canonization | Interval hypergraphs | Unit interval graphs | interval hypergraphs | MATHEMATICS, APPLIED | convex graphs | ISOMORPHISM | EFFICIENT PARALLEL ALGORITHMS | LINEAR-TIME RECOGNITION | PROPERTY | graph canonization | unit interval graphs | proper interval graphs | graph isomorphism | COMPUTER SCIENCE, THEORY & METHODS | logspace | interval graphs | IDENTIFICATION MATRICES

Interval graphs | Convex graphs | Graph isomorphism | Logspace | Proper interval graphs | Graph canonization | Interval hypergraphs | Unit interval graphs | interval hypergraphs | MATHEMATICS, APPLIED | convex graphs | ISOMORPHISM | EFFICIENT PARALLEL ALGORITHMS | LINEAR-TIME RECOGNITION | PROPERTY | graph canonization | unit interval graphs | proper interval graphs | graph isomorphism | COMPUTER SCIENCE, THEORY & METHODS | logspace | interval graphs | IDENTIFICATION MATRICES

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2018, Volume 32, Issue 1, pp. 148 - 172

A matching M in a graph G is said to be uniquely restricted if there is no other matching in G that matches the same set of vertices as M. We describe a...

Interval graph | Weak independent set | Bipartite permutation graph | Uniquely restricted matching | Interval nest digraph | Proper interval graph | proper interval graph | MATHEMATICS, APPLIED | uniquely restricted matching | weak independent set | PERMUTATION GRAPHS | RECOGNITION | ALGORITHMS | DIGRAPHS | bipartite permutation graph | interval nest digraph | interval graph

Interval graph | Weak independent set | Bipartite permutation graph | Uniquely restricted matching | Interval nest digraph | Proper interval graph | proper interval graph | MATHEMATICS, APPLIED | uniquely restricted matching | weak independent set | PERMUTATION GRAPHS | RECOGNITION | ALGORITHMS | DIGRAPHS | bipartite permutation graph | interval nest digraph | interval graph

Journal Article

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2018, Volume 10755, pp. 8 - 19

Conference Proceeding

Algorithmica, ISSN 0178-4617, 4/2019, Volume 81, Issue 4, pp. 1490 - 1511

In 1969, Roberts introduced proper and unit interval graphs and proved that these classes are equal. Natural generalizations of unit interval graphs called k...

Interval graphs | Computer Systems Organization and Communication Networks | Algorithms | Proper and unit interval graphs | Mathematics of Computing | Computer Science | Partial representation extension | Theory of Computation | Algorithm Analysis and Problem Complexity | Recognition | Data Structures and Information Theory | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED

Interval graphs | Computer Systems Organization and Communication Networks | Algorithms | Proper and unit interval graphs | Mathematics of Computing | Computer Science | Partial representation extension | Theory of Computation | Algorithm Analysis and Problem Complexity | Recognition | Data Structures and Information Theory | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 08/2019, Volume 267, pp. 52 - 63

A poset P=(X,≺) has an interval representation if each x∈X can be assigned a real interval Ix so that x≺y in P if and only if Ix lies completely to the left of...

Interval order | Interval graph | Semiorder | MATHEMATICS, APPLIED | GRAPHS | Set theory | Polynomials | Representations | Weight

Interval order | Interval graph | Semiorder | MATHEMATICS, APPLIED | GRAPHS | Set theory | Polynomials | Representations | Weight

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 05/2019, Volume 260, pp. 256 - 261

For a graph G and an integer-valued threshold function τ on its vertex set, a dynamic monopoly is a set of vertices of G such that iteratively adding to it...

Interval graph | Dynamic monopoly | Target set selection | MATHEMATICS, APPLIED | Monopolies | Graphs | Polynomials | Apexes | Mathematical analysis

Interval graph | Dynamic monopoly | Target set selection | MATHEMATICS, APPLIED | Monopolies | Graphs | Polynomials | Apexes | Mathematical analysis

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 02/2020, Volume 806, pp. 197 - 218

We investigate for temporal graphs the computational complexity of separating two distinct vertices s and z by vertex deletion. In a temporal graph, the vertex...

Temporal paths | Dynamic programming | Temporal restrictions | Fixed-parameter tractability | Unit interval graphs | NP-completeness | COMPLEXITY | COMPUTER SCIENCE, THEORY & METHODS

Temporal paths | Dynamic programming | Temporal restrictions | Fixed-parameter tractability | Unit interval graphs | NP-completeness | COMPLEXITY | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

ACM Transactions on Algorithms (TALG), ISSN 1549-6325, 07/2018, Volume 14, Issue 3, pp. 1 - 62

In the I nterval C ompletion problem we are given an n -vertex graph G and an integer k , and the task is to transform G by making use of at most k edge...

completion problems | interval graphs | Subexponential algorithms | graph modification problems

completion problems | interval graphs | Subexponential algorithms | graph modification problems

Journal Article

Information Processing Letters, ISSN 0020-0190, 06/2019, Volume 146, pp. 27 - 29

•The eternal domination and clique-connected cover numbers coincide for interval graphs.•The previous proof of this fact for proper interval graphs is greatly...

Interval graphs | Combinatorial problems | Eternal dominating set | Neocolonization | COMPUTER SCIENCE, INFORMATION SYSTEMS | Algorithms

Interval graphs | Combinatorial problems | Eternal dominating set | Neocolonization | COMPUTER SCIENCE, INFORMATION SYSTEMS | Algorithms

Journal Article

09/2017

Involve 11 (2018) 893-900 A poset $P= (X, \prec)$ has an interval representation if each $x \in X$ can be assigned a real interval $I_x$ so that $x \prec y$ in...

Mathematics - Combinatorics

Mathematics - Combinatorics

Journal Article

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