Connecting rank-width and tree-width via pivot-minors = Pivot-minor들을 이용한 rank-width와 tree-width의 관계에 대한 연구

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We prove that every graph of rank-width $k$ is a pivot-minor of a graph of tree-width at most $2k$ and every graph of linear rank-width $k$ is a pivot-minor of a graph of path-width at most $k+1$. We also prove that graphs of rank-width at most $1$ are exactly vertex-minors of trees, and graphs of linear rank-width at most $1$ are precisely vertex-minors of paths. In addition, we show that bipartite graphs of rank-width at most $1$ are exactly pivot-minors of trees and bipartite graphs of linear rank-width at most $1$ are precisely pivot-minors of paths. Also, we calculate the linear rank-width of complete binary trees. And we show that if a tree has linear rank-width at least $k$, then it has the complete binary tree of height $k$ as a vertex-minor. Finally, we describe an interesting question that a class of graphs with unbounded linear rank-width contains all trees as vertex-minors or pivot-minors. We prove that this question for pivot-minor is false and we suggest another version of the question.
Advisors
Oum, Sang-Ilresearcher엄상일
Description
한국과학기술원 : 수리과학과,
Publisher
한국과학기술원
Issue Date
2012
Identifier
509386/325007  / 020104251
Language
eng
Description

학위논문(석사) - 한국과학기술원 : 수리과학과, 2012.8, [ iv, 29 p. ]

Keywords

rank-width; tree-width; vertex-minor; rank-width; tree-width; vertex-minor; pivot-minor; pivot-minor

URI
http://hdl.handle.net/10203/181586
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=509386&flag=dissertation
Appears in Collection
MA-Theses_Master(석사논문)
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