CAJ | 학술논문

令G=(V(G),E(G))是一个图,并令g和f是两个定义在V(G)上的整数值函数且对所有的x∈V(G)有g(x)≤f(x)成立.若对G的每一条边e都存在G的一个分数(g,f)-因子Gh使得h(e)=0,其中h是Gh的示性函数,则称G是一个分数(g,f)-消去图.若在G中删去E'(∩-)E(G),|E'|=k后,所得图有分数完美匹配,则称G是分数k-边-可消去的.本文给出了图是1-可消去,2-可消去和k-边-可消去的与韧度和孤立韧度相关的充分条件,证明了这些结果在一定意义上是最好可能的.
령G=(V(G),E(G))시일개도,병령g화f시량개정의재V(G)상적정수치함수차대소유적x∈V(G)유g(x)≤f(x)성립.약대G적매일조변e도존재G적일개분수(g,f)-인자Gh사득h(e)=0,기중h시Gh적시성함수,칙칭G시일개분수(g,f)-소거도.약재G중산거E'(∩-)E(G),|E'|=k후,소득도유분수완미필배,칙칭G시분수k-변-가소거적.본문급출료도시1-가소거,2-가소거화k-변-가소거적여인도화고립인도상관적충분조건,증명료저사결과재일정의의상시최호가능적.
Let G=(V(G), E(G)) be a graph, and let g, f be two integer-valued functions defined on V(G) such that g(x) ≤ f(x) for all x ∈ V(G). G is called fractional (g, f)-deleted if for each edge e of G, there exists a fractional (g, f)-factor Gh such that h(e) = 0, where h is the indicator function of Gh. G is called fractional k-edge-deleted if deleting E' (∩-) E(G), |E'| = k, there exists a fractional perfect matching. In this paper, sufficient conditions related to toughness and isolated toughness for a graph to be fractional 1-deleted, 2-deleted and k-edge-deleted are given. The results are proved to be best possible in some sense.