【摘要】 <正> 则称f_T为T的一个愉快标号,称T为一棵愉快树. A.Kotxig猜想:每一棵树都能愉快标号.这是图论中至今未能解决的难题之一.目前已经证明的只是很少几类特殊的树,本文给出愉快串接定理,并在此定理的基础上得出几类愉快树. 定义 若树T存在一个分划π=(A(T),B(T))和愉快标号f_T,其中π满足:更多还原

【Abstract】 The article gives a definition of pleasant stringing trees and proves that the treesthat are stringed together by any pleasant stringing trees at their joints and verticesof the greatest mark are pleasant trees. It also proves that 1) the trees stringed to-gether by any pleasant stringing trees and any eaterpillar-trees are pleasant trees; 2)the trees to which some edges are joined at the joint and vertex of the greates markare pleasant stringing trees; 3) the trees joined by two isomorphic pleasant trees attheir vertices of the greatest mark (defined as double isomorphic pleasant trees) arealso pleasant stringing trees. With the above result, the article comes to a conclusionthat ladder-trees and mountain-trees are pleasant trees and that the trees stringed to-gether by double isomorphic pleasant trees, other known pleasant stringing trees andcaterpillar-trees are pleasant trees.更多还原