Abstract Vizing’s conjecture from 1968 asserts that the domination number of the Cartesian product of two graphs is at least as large as the product of their domination numbers. We prove that for any claw-free graph G and an arbitrary graph H , the inequality γ ( G □ H ) ≥ 3 4 γ ( G ) γ ( H ) always holds.

中文翻译：

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无爪图的 Vizing 猜想的 34 近似

摘要 Vizing 1968 年的猜想断言，两个图的笛卡尔积的支配数至少与它们的支配数的乘积一样大。我们证明，对于任何无爪图 G 和任意图 H ，不等式 γ ( G □ H ) ≥ 3 4 γ ( G ) γ ( H ) 始终成立。