Seminar on Combinatorics
主講者: 徐力行教授 (靜宜大學資工系)
講題: Solution to an open problem on 4-ordered Hamiltonian graphs
時間: 2012-01-13 (Fri.)  10:30 - 11:30
地點: 數學所 617 研討室 (台大院區)
Abstract: A graph G is k-ordered if for any sequence of k distinct vertices of G, there exists a cycle in G containing these k vertices in the speci ed order. It is k-ordered Hamiltonian if, in addition, the required cycle is Hamiltonian. The question of the existence of an in nite class of 3-regular 4-ordered Hamiltonian graphs was posed in 1997. At the time, the only known examples were K4 and K3;3. Some progress was made in 2008 when the Peterson graph was found to be 4-ordered and the Heawood graph was proved to be 4-ordered Hamiltonian; moreover an in nite class of 3-regular 4-ordered graphs was found. In this paper we show that a subclass of generalized Petersen graphs are 4-ordered and give a complete classi cation for which of these graphs are 4-ordered Hamiltonian. In particular, this answers the open question regarding the existence of an in nite class of 3-regular 4-ordered Hamiltonian graphs. Moreover, a number of results related to other open problems are presented.
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