DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Oum, Sang-Il | - |
dc.contributor.advisor | 엄상일 | - |
dc.contributor.author | Jeong, Ji-Su | - |
dc.contributor.author | 정지수 | - |
dc.date.accessioned | 2015-04-29 | - |
dc.date.available | 2015-04-29 | - |
dc.date.issued | 2013 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=566482&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/198118 | - |
dc.description | 학위논문(석사) - 한국과학기술원 : 수리과학과, 2013.8, [ ii, 34 p. ] | - |
dc.description.abstract | The minimum rank of a graph $G$ over a field $\F$ is the smallest possible rank of an $n\times n$ symmetric matrix whose $(i,j)$-entry is nonzero if and only if two vertices $i$ and $j$ are adjacent in $G$ for $i\neq j$. A random graph $G(n,p)$ is a graph on a vertex set $\{1,2,\cdots,n\}$ such that two vertices are adjacent independently at random with probability $p$. First, we investigate the minimum rank of a random graph over the binary field $\F_2$. We prove that the minimum rank of a random graph $G(n,1/2)$ over the binary field is at least $n-\sqrt{2n}-1.1$ asymptotically almost surely. Also, we prove that if $p(n)$ is a function such that $0<p(n)\le\frac{1}{2}$ and $np(n)$ is increasing, then the minimum rank of a random graph $G(n,p(n))$ over the binary field is at least $n-1.178\sqrt{n/p(n)}$ asymptotically almost surely. Second, we show that for a fixed positive integer $k$ and a fixed finite field $\F_q$, there exists $O(\abs{V(G)}^2)$-time algorithm that decides whether the input graph $G$ has the minimum rank over $\F_q$ at most $k$. We have three different proofs using a monadic second-order logic, dynamic programming, or a kernelization. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | fixed-parameter tractable algorithm | - |
dc.subject | random graph | - |
dc.subject | 랜덤 그래프 | - |
dc.subject | minimum rank | - |
dc.subject | 알고리즘 | - |
dc.title | On the minimum rank of a graph | - |
dc.title.alternative | 그래프의 minimum rank에 대하여 | - |
dc.type | Thesis(Master) | - |
dc.identifier.CNRN | 566482/325007 | - |
dc.description.department | 한국과학기술원 : 수리과학과, | - |
dc.identifier.uid | 020114487 | - |
dc.contributor.localauthor | Oum, Sang-Il | - |
dc.contributor.localauthor | 엄상일 | - |
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