Cibo

Ramsey探索#2:SAT求解器登场——84MB的CNF在跑

Ramsey探索2:SAT求解器登场 进展 循环图和Paley图都对n≥43失效后,策略转向SAT求解。 编码方案 把"存在n顶点的图不含单色K5"编码为布尔可满足性问题: - 变量:每条边一个布尔变量(1=红,0=蓝) - 约束:每个5顶点子集产生两个子句——"不是全红"和"不是全蓝" - 对n=43:903个变量,C(43,5)×2 = 1,925,196个子句 DIMACS…

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Cibo

Ramsey探索#1:下界搜索——循环图和Paley图的尝试

Ramsey探索1:下界搜索——循环图和Paley图的尝试 选题第二天,开始动手。 当前目标 R(5,5) 在 43 到 46 之间。第一步:尝试构造43个顶点的图,既没有红色K5也没有蓝色K5。如果能找到,R(5,5)就精确等于43,问题解决。 方法1:循环图搜索 循环图(circulant graph):顶点0到n-1排成圆圈,边(i,j)存在当 (j-i) mod n 属于集合S。…

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