Suured indutseeritud metsad tasandilistes graafides
| dc.contributor.advisor | Theis, Dirk Oliver | |
| dc.contributor.advisor | Khoshkhah, Kaveh | |
| dc.contributor.author | Hennoch, Kairi | |
| dc.date.accessioned | 2017-04-26T07:12:30Z | |
| dc.date.available | 2017-04-26T07:12:30Z | |
| dc.date.issued | 2016 | |
| dc.description.abstract | Tasandilised graafid on graafid, mida saab joonistada tasandile nii, et tema servad ei lõiku üksteisega mujal kui tippudes. Selles töös me uurime, kui suuri indutseeritud metsi on alati võimalik tasandilistes graafides leida. Praegu parim teadaolev tulemus on pärit Borodinilt, mille kohaselt igas tasandilises graafis leidub indutseeritud mets, mis sisaldab vähemalt 2/5 tema tippudest. Selles tööd anname me osalise tulemuse selle hinnangu parandamise suunas. Täpsemalt, me näitame, et minimaalne vastunäide meie parandatud tulemusele ei sisalda tippe, mille aste on väiksem kui 4, ja et selles sisalduvad astmega 4 tipud saavad olla vaid üht kindlat tüüpi. | |
| dc.description.abstract | Planar graphs are graphs that can be drawn on a plane so that its edges do not cross each other (other that at their endpoints). In this thesis, we study the size of induced forests in planar graphs. The current best result by Borodin states that every planar graph has an induced forest that contains at least 2/5 of its vertices. In this thesis, we give partial results towards improving this bound. Specifically, we show that a minimal counterexample to an improved bound has minimal degree at least 3 and can contain only a specific type of vertices with degree 4. | |
| dc.identifier.uri | http://hdl.handle.net/10062/56197 | |
| dc.language.iso | eng | |
| dc.title | Suured indutseeritud metsad tasandilistes graafides | |
| dc.title.alternative | Large Induced Forests in Planar Graphs | |
| dc.type | Thesis |
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