【摘要】 为了寻找一类具有任意大色数但不含三角形的图类, Mycielski提出一种有趣的图变换,即把图G变为一种新的图类μ(G),称之为图G的Mycielskian图.对于任意的正整数m,图G的广义Mycielskian图μ_m(G)是图G的Mycielskian图的一种自然推广.本文主要研究了广义Mycielskian图μ_m(G)的哈密顿性和与匹配相关的因子临界性.更多还原

【Abstract】 In a search for triangle-free graphs with arbitrarily large chromatic number,Mycielski developed a graph transformation that transforms a graph G into a new graphμ(G), which is called the Mycielskian of G. A generalisation of this transformation is the generalised Mycielskian, denoted by μ_m(G), where m is a positive integer. This paper investigates the hamiltonicity and some matching-related properties of generalized Mycielskian μ_m(G).更多还原