CAJ | 학술논문

设S是连通图G的一个边割。若G-S不包含孤立点，则称S是G的一个限制边割。图G的最小限制边割的边数称为G的限制边连通度，记为λ'（ G）.如果图G的限制边连通度等于其最小度，则称图G是最优限制边连通的，简称λ'-最优的。设G是一个n阶的连通无三角图，且最小度δ（G）≥2.文章证明了，若最小边度ξ（G）≥ n2(-2)(1＋（δ G1）-1)，则G是λ'-最优的。并由此推出，若连通无三角图G的最小度δ（G）≥ n4＋1，则G是λ'-最优的。最后给出例子说明这些结果给出的边界都是紧的。
설S시련통도G적일개변할。약G-S불포함고립점，칙칭S시G적일개한제변할。도G적최소한제변할적변수칭위G적한제변련통도，기위λ'（ G）.여과도G적한제변련통도등우기최소도，칙칭도G시최우한제변련통적，간칭λ'-최우적。설G시일개n계적련통무삼각도，차최소도δ（G）≥2.문장증명료，약최소변도ξ（G）≥ n2(-2)(1＋（δ G1）-1)，칙G시λ'-최우적。병유차추출，약련통무삼각도G적최소도δ（G）≥ n4＋1，칙G시λ'-최우적。최후급출례자설명저사결과급출적변계도시긴적。
An edge cut S of a connected graph G is called as a restricted edge cut,if G-S contains unisolated verti-ces. The minimum cardinality of all restricted edge cuts is called as the restricted edge connectivity of λ'( G). A graph G is optimally restricted edge-connected,for shortλ'-optimal,ifλ'( G)=ξ( G),whereξ( G)is the minimum edge degree of G. A graph is thought to be super-restricted edge-connected,for short super-λ' if every minimum re-stricted edge cut isolates an edge. Let G be a connected triangle-free graph of order n and minimum degree δ( G≥2),if the minimum edge degree ξ(G)≥ n( 2-2) 1+(δ 1G)-( 1),then G is λ'-optimal. Using this result,we deduce that if the minimum degree of triangle-free graph G,δ( G)≥n4 +1,then G is λ'-optimal. Finally,an example is presented to show that the bounds of these results are both tight.