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Alliance free sets in Cartesian product graphs
Let G = (V,E) be a graph. For a non-empty subset of vertices S ⊆ V , and vertex v ∈ V , let δS(v) = |{u ∈ S : uv ∈ E}| denote the cardinality of the set of neighbors of v in S, and let S = V − S. Consider the following condition: δS(v) ≥ δS(v) + k, (1) which states that a vertex v has at least k more neighbors in S than it has in S. A set S ⊆ V that satisfies Condition (1) for every vertex v ∈ ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1950
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1950-0037893-9