Graph decompositions and related extremal problems = 그래프 분할과 관련된 극단 문제

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We present several results on graph decompositions and related extremal problems. The first result discusses the decomposition of graphs with no odd complete minor, the second result investigates how minor-monotone changes after adding a few random edges, and how the structure of a given graph changes after these random edge perturbations. The third and fourth results focus on directed graphs and their extremal properties, and study how many edges can be deleted while preserving the vertex/edge-connectivity of a given highly connected tournament-like digraph, or how a highly connected tournament-like digraph can be partitioned into many highly connected pieces with desired shapes. The last result is related to the rational exponent conjecture by Erdős and Simonovits in 1980s, which studies how many edges an $n$-vertex graph $G$ can have if $G$ does not contain a bipartite graph $H$ as a subgraph, and the exponents of these extremal functions.
Advisors
Oum, Sang-ilresearcher엄상일researcher
Description
한국과학기술원 :수리과학과,
Publisher
한국과학기술원
Issue Date
2020
Identifier
325007
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2020.2,[v, 145 p. :]

Keywords

Graph Decomposition▼aExtremal graph theory▼aGraph minor▼aRandom graphs▼aTournaments▼aDirected graphs▼aFour colour theorem▼aChromatic number▼aRational exponent conjecture; 그래프 분할▼a극단 그래프 이론▼a그래프 마이너▼a랜덤 그래프▼a토너먼트▼a방향 그래프▼a4색 정리▼a채색수▼a유리수 차수 추측

URI
http://hdl.handle.net/10203/283585
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=907856&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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