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National Research University Higher School of EconomicsStudent ThesesSeveral Sweeps Algorithms for Recognizing Two Types of Interval Graphs

Student
Title
Supervisor
Faculty
Educational Programme
Final Grade
Year of Graduation
Victoria Belous
Several Sweeps Algorithms for Recognizing Two Types of Interval Graphs
Applied Mathematics and Information Science
(Master’s programme)
7
2016
Interval graphs - one of the types of intersection graphs. The aim of this thesis is to study the algorithms of recognition interval and unit interval graphs, to implement them in the form of a computer program and conduct test calculations on graphs.

Interval Count - Count intersections of a plurality of intervals on the line. In other words, the interval graph vertices are some intervals on the line and any two vertices are connected by an edge if and only if their corresponding intervals intersect.

Each interval graph is chordal. A graph is chordal if each of its cycles, having four or more arcs have a chord, which is an edge connecting the two vertices are not adjacent in the cycle. An equivalent definition - if any cycle without chords has a maximum of three ribs.

The unit interval graphs - graph intersection intervals of the same length.

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