A Neighborhood Union Condition for Fractional ID-[a, b]-factor-critical Graphs  

作　　者：Yuan YUAN Rong-Xia HAO 

机构地区：[1]Department of Mathematics, Beijing Jiaotong University

出　　处：《Acta Mathematicae Applicatae Sinica》2018年第4期775-781,共7页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11371052,11731002);the Fundamental Research Funds for the Central Universities(Nos.2016JBM071,2016JBZ012);the 111 Project of China(B16002)

摘　　要：Let a, b, r be nonnegative integers with 1 ≤ a ≤ b and r ≥ 2. Let G be a graph of order n with n 〉（a＋2 b）（r（a＋b）-2）/b.In this paper, we prove that G is fractional ID-[a, b]-factor-critical if δ（G）≥bn/a＋2 b＋a（r-1）and ｜NG（x1） ∪ NG（x2） ∪…∪ NG（xr）｜ ≥（a＋b）n/（a＋2 b） for any independent subset {x1,x2,…,xr} in G. It is a generalization of Zhou et al.＇s previous result [Discussiones Mathematicae Graph Theory, 36： 409-418（2016）]in which r = 2 is discussed. Furthermore, we show that this result is best possible in some sense.Let a, b, r be nonnegative integers with 1 ≤ a ≤ b and r ≥ 2. Let G be a graph of order n with n 〉（a＋2 b）（r（a＋b）-2）/b.In this paper, we prove that G is fractional ID-[a, b]-factor-critical if δ（G）≥bn/a＋2 b＋a（r-1）and ｜NG（x1） ∪ NG（x2） ∪…∪ NG（xr）｜ ≥（a＋b）n/（a＋2 b） for any independent subset {x1,x2,…,xr} in G. It is a generalization of Zhou et al.＇s previous result [Discussiones Mathematicae Graph Theory, 36： 409-418（2016）]in which r = 2 is discussed. Furthermore, we show that this result is best possible in some sense.

关 键 词：GRAPH minimum degree NEIGHBORHOOD fractional [a b]-factor fractional ID-[a b]-factor-critical 

分 类 号：O157.5[理学—数学]