Hadwiger's conjecture and its variants하트비거의 추측과 그에 대한 변형

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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.
Advisors
Oum, Sang-ilresearcher엄상일researcher
Description
한국과학기술원 :수리과학과,
Publisher
한국과학기술원
Issue Date
2016
Identifier
325007
Language
eng
Description

학위논문(석사) - 한국과학기술원 : 수리과학과, 2016.2 ,[iii, 23 p. :]

Keywords

hadwiger; coloring; minor; graph; odd minor; 하트비거; 채색; 마이너; 그래프; 홀수 마이너

URI
http://hdl.handle.net/10203/221545
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=649505&flag=dissertation
Appears in Collection
MA-Theses_Master(석사논문)
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