On Kotzig's conjecture concerning graphs with a unique regular path-connectivity

被引：1

作者：

Yang, YS ^{[1
]}

Lin, JH

Wang, CL

Li, KF

机构：

[1] Dalian Univ Technol, Dept Comp Engn & Sci, Dalian 116024, Peoples R China

[2] Dalian Univ Technol, Dept Math, Dalian 116024, Peoples R China

来源：

DISCRETE MATHEMATICS | 2000年 / 211卷 / 1-3期

基金：

中国国家自然科学基金;

关键词：

regular path-connectivity; Eulerian graph;

D O I：

10.1016/S0012-365X(99)00153-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Kotzig (see Bendy and Murty, Graph Theory with Applications, North-Holland, Amsterdam, 1976) conjectured that there exists no graph with the property that every pair of vertices is connected by a unique path of length k, k > 2. Kotzig (Graph Theory and Related Topics, Academic Press, New York, 1979, pp. 358-367) has proved this conjecture for 2 < k < 9. Xing and Hu (Discrete Math. 135 (1994) 387-393) have proved it for k > 11. Here we prove this conjecture for the remaining cases k = 9, 10, 11. (C) 2000 Elsevier Science B.V. All rights reserved.

引用

页码：287 / 298

页数：12