Partitions, I
نویسندگان
چکیده
منابع مشابه
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Let us consider S1, S2. We introduce S1 b S2 and S2 c S1 as synonyms of S1 is finer than S2. The following four propositions are true: (3)1 ⋃ (S1 \{ / 0}) = ⋃ S1. (4) For all partitions P1, P2 of Y such that P1 c P2 and P2 c P1 holds P2 ⊆ P1. (5) For all partitions P1, P2 of Y such that P1 c P2 and P2 c P1 holds P1 = P2. (7)2 For all partitions P1, P2 of Y such that P1 c P2 holds P1 is coarser ...
متن کاملA Theory of Partitions . Part I
For simplicity, we use the following convention: Y is a non empty set, P1, P2 are partitions of Y , A, B are subsets of Y , i is a natural number, x, y, x1, x2, z0 are sets, and X, V , d, t, S1, S2 are sets. The following proposition is true (1) If X ∈ P1 and V ∈ P1 and X ⊆ V, then X = V. Let us consider S1, S2. We introduce S1 ⋐ S2 and S2 ⋑ S1 as synonyms of S1 is finer than S2. We now state s...
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A set $S = {u_1,u_2, ldots, u_t}$ of vertices of $G$ is an efficientdominating set if every vertex of $G$ is dominated exactly once by thevertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$%, we note that ${U_1, U_2, ldots U_t}$ is a partition of the vertex setof $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices atdistance~1 from it in $G$. In this ...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1968
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1968.100809