标题： Hoffman 的可着色性（强）正则图 显示英文标题

标题： Hoffman colorability of (strongly) regular graphs

摘要： 霍夫曼界是一个已知的图的色数的特征值界。 通过将这个界视为一个参数，我们展示了达到该界的着色（霍夫曼着色）在几种图正则性概念中的多个应用：正则、（共）边正则和强正则。 对于强正则图，我们证明了霍夫曼可着色性意味着伪几何性，并通过考虑霍夫曼界而不是色数，加强了哈默斯关于具有有界色数的强正则图的有限性结果。 此外，通过使用霍夫曼着色，我们表明Godsil、Roberson、Rooney、Šámal和Varvitsiotis [欧洲组合杂志 79, 2019] 所展示的非唯一向量着色性的充分条件在强正则图的设置中可以被放松。 最后，利用霍夫曼着色，我们得出了上述图正则性概念的几个新特征。 显示英文摘要

摘要： Hoffman's bound is a well-known eigenvalue bound on the chromatic number of a graph. By interpreting this bound as a parameter, we show multiple applications of colorings attaining the bound (Hoffman colorings) for several notions of graph regularity: regular, (co-)edge-regular, and strongly regular. For strongly regular graphs, we prove that Hoffman colorability implies pseudo-geometricity, and we strengthen Haemers' finiteness result on strongly regular graphs with a bounded chromatic number by considering the Hoffman bound instead of the chromatic number. Furthermore, by using Hoffman colorings we show that a sufficient condition for non-unique vector colorability shown by Godsil, Roberson, Rooney, \v{S}\'amal and Varvitsiotis [European J. Combin. 79, 2019] can be relaxed in the setting of strongly regular graphs. Lastly, using Hoffman colorings we derive several new characterizations of the mentioned graph regularity notions.