DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Oum, Sang-il | - |
dc.contributor.advisor | 엄상일 | - |
dc.contributor.author | Kang, Dong Yeap | - |
dc.contributor.author | 강동엽 | - |
dc.date.accessioned | 2017-03-29T02:34:52Z | - |
dc.date.available | 2017-03-29T02:34:52Z | - |
dc.date.issued | 2016 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=649505&flag=dissertation | en_US |
dc.identifier.uri | http://hdl.handle.net/10203/221545 | - |
dc.description | 학위논문(석사) - 한국과학기술원 : 수리과학과, 2016.2 ,[iii, 23 p. :] | - |
dc.description.abstract | Hadwiger's conjecture, which is one of the infamous conjectures in graph theory, states that for $t \geq 1$, every graph with no $K_t$ as a minor is (t-1)-colourable. Gerards and Seymour strengthened this conjecture, that every graph with no $K_t$ as an odd minor is (t-1)-colourable. We are interested in variants of both conjectures, in terms of an improper colouring: for $t \geq 1$, is there an integer D such that every graph G with no $K_t$ minor (odd minor) has a vertex partition into k(t) parts so that every subgraph induced on each partition has the maximum degree at most D? For graphs with no $K_t$ minor, Edwards, Kim, Oum, Seymour, and the author proved k(t) = t-1 for $t \geq 1$, and this is sharp. With the essentially same proof, this holds for graphs with no bipartite $K_t$ subdivision. For graphs with no odd $K_t$ -minor, Oum and the author proved k(t) = 7t - 10 for $t \geq 2$. Using some previous results, this improves the result by Kawarabayashi. | - |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | hadwiger | - |
dc.subject | coloring | - |
dc.subject | minor | - |
dc.subject | graph | - |
dc.subject | odd minor | - |
dc.subject | 하트비거 | - |
dc.subject | 채색 | - |
dc.subject | 마이너 | - |
dc.subject | 그래프 | - |
dc.subject | 홀수 마이너 | - |
dc.title | Hadwiger's conjecture and its variants | - |
dc.title.alternative | 하트비거의 추측과 그에 대한 변형 | - |
dc.type | Thesis(Master) | - |
dc.identifier.CNRN | 325007 | - |
dc.description.department | 한국과학기술원 :수리과학과, | - |
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