| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Outline of Final Research Achievements |
Let a, b and r be positive integers such that a+b=r and a≦r/2. We want to prove the following conjecture: If r is odd, then every r-regular graph has an {a,b}-factor. We showed that if either a is even or a is odd and r/3≦a≦r/2, then the conjecture holds. On the other, it was recently shown that the conjecture does not hold if (a+1)(a+2)≦r. However there are unsolved cases. We also obtained some results on factors of graphs and spanning trees of graph, which are related to the above conjecture.
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