Title :
A problem on claw-free homogeneously traceable
Author :
Li, Zu ; Ke-Wen Zhao ; Lin, Yue ; Chen, De-Qin
Author_Institution :
Inst. of Inf. Sci. & Math., Univ. of Qiongzhou, Sanya, China
Abstract :
In 1988 Faudree et al. proved that let G be a 3-connected K1,3-free graph of order n, if |N(x)∪ N(y)|≥(2n-4)/3 for each pair of nonadjacent vertices x,y, then G is Homogeneously traceable. In 1991nian Bauer et al. proved that let G be a 3-connected K1,3-free graph of order n, if |N(x) ∪ N(y)|≥(2n-5)/3 for each pair of nonadjacent vertices x,y, then G is traceable. In this note we prove the further result: let G be a 3-connected K1,3-free graph of order n, if |N(x) ∪ N(y)|≥(2n-6)/3 for each pair of nonadjacent vertices x,y with 1≤|N(x) ∩ N(y)|≤α-1, then G is Homogeneously traceable.
Keywords :
graph theory; claw-free homogeneously traceable; free graph of order; nonadjacent vertices; Artificial neural networks; Generalizing neighborhood unions; Homogeneously traceable; K1,3—free graphs; Neighborhood unions; traceable;
Conference_Titel :
Industrial Engineering and Engineering Management (IE&EM), 2010 IEEE 17Th International Conference on
Conference_Location :
Xiamen
Print_ISBN :
978-1-4244-6483-8
DOI :
10.1109/ICIEEM.2010.5646538