| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
Thomassen's conjecture is that any 4-edge connected line graph has a Hamilton cycle. This conjecture is equivalent to the following conjecture: any essentially 4-edge connected graph has a edge dominating cycle. In this research, we mainly studied followings: 1. existence of 2-factors in 4-edge connected line graphs which has properties weaker than properties of Hamilton cycles and 2. existence of Tutte closed trails in any essentially 4-edge connected graph. In consequence, we obtained followings: 1. the relation and the equivalence on Thomassen's conjecture and Bondy's conjecture and 2. in essentially 3-edge connected cubic graphs, the existence and the number of connected components of spanning subgraphs in which every connected components are closed trails. Such spanning subgraphs generalizes 2-factors. The third result improve the results by Yoshimoto and Bill Jackson on the number of connected components of essentially 3-edge connected cubic graphs.
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