We introduce the concept of the primitivity of independent set in vertex-transitive graphs, and investigate the relationship between the primitivity and the structure of maximum independent sets in direct products of vertex-transitive graphs. As a consequence of our main results, we positively solve
The Resolution Complexity of Independent Sets and Vertex Covers in Random Graphs
β Scribed by Paul Beame; Russell Impagliazzo; Ashish Sabharwal
- Publisher
- Springer
- Year
- 2007
- Tongue
- English
- Weight
- 486 KB
- Volume
- 16
- Category
- Article
- ISSN
- 1016-3328
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## Abstract Let __G__ be a connected, nonbipartite vertexβtransitive graph. We prove that if the only independent sets of maximal cardinality in the tensor product __G__ Γ __G__ are the preimages of the independent sets of maximal cardinality in __G__ under projections, then the same holds for all
Generalizing a theorem of Moon and Moser. we determine the maximum number of maximal independent sets in a connected graph on n vertices for n sufficiently large, e.g., n > 50. = I .32. . .). Example 1.2. Let b, = i(C,), where C,z denotes the circuit of length n. Then b, = 3, 6, = 2, b, = 5, and b,