Charakterizace DAG-depth orientovaného grafu

Bc. Matúš Bezek

Bachelor's thesis

Characterizing DAG-depth of directed graphs

Abstract:

Študujeme DAG-depth, štrukturálnu hĺbkovú mieru orientovaných grafov, ktorá prirodzene rozširuje tree-depth neorientovaných grafov. Definujeme DAG-depth dekompozíciu ako policajnú stratégiu vo verzii hry na policajtov a zlodeja, kde položený policajt ostane v danom vrchole do konca hry. DAG-depth dekompozícia sa vzťahuje k DAG-depth podobne ako eliminačný strom k tree-depth. Poskytujeme definíciu zlúčiteľných a optimálne zlúčiteľných vrcholov s cieľom zmenšiť dekompozíciu aby bola prijateľná ako policajná stratégia. Takisto definujeme uzáver, ktorý udáva najväčší graf na ktorom daná dekompozícia predstavuje víťaznú policajnú stratégiu.

Abstract:

We study DAG-depth, a structural depth measure of directed graphs, which naturally extends the tree-depth of ordinary graphs. We define a DAG-depth decomposition as a strategy for the cop player in the lift-free version of the cops-and-robber game on directed graphs. The DAG-depth decomposition is related to DAG-depth in a similar way as an elimination tree is related to the tree-depth. We provide a definition of the mergeable and optimally mergeable vertices in order to make the decomposition smaller and acceptable for the cop player as a strategy. We also define a closure, which gives the largest digraph for which the given decomposition represents a winning strategy for the cop player.

Keywords

DAG-depth, DAG-depth decomposition, graph theory, directed graph, cops-and-robber, DAG-depth dekompozícia, teória grafov, orientované grafy, hra na policajtov a zlodeja

Language used: English

Date on which the thesis was submitted / produced: 19. 5. 2016

Thesis defence

• Date of defence: 22. 6. 2016
• Supervisor: prof. RNDr. Petr Hliněný, Ph.D.
• Reader: doc. Mgr. Jan Obdržálek, PhD.

Masaryk University

Faculty of Informatics

Bachelor programme / field:
Informatics / Mathematical Informatics