Cycle-connected graphs

On 4-connected graphs without even cycle decompositions

Small cycle covers of 3-connected cubic graphs

Every 2-connected simple cubic graph of order n ≥ 6 has a cycle cover with at most dn4 e cycles. This bound is best possible.

A cycle embedding problem for Cube-Connected Cycles Graphs

Let n be an odd integer with n ≥ 3. The cube-connected cycles graph CCCn has n × 2 vertices, labeled (l,x), where 0 ≤ l ≤ n − 1 and x is an n-bit binary string. Two vertices (l,x) and (l′,y) are adjacent if and only if either x = y and |l − l′| = 1, or l = l′ and y = (x). In this paper, we will find the set of all possible lengths of cycles in CCCn with n is odd and n ≥ 3 .

Small cycle cover of 2-connected cubic graphs

Every 2-connected simple cubic graph of order n¿ 6 has a cycle cover with at most n=4 cycles. This bound is best possible. c © 2003 Elsevier B.V. All rights reserved.

A characterization of 1-cycle resonant graphs among bipartite 2-connected plane graphs

It is proved that a bipartite 2-connected plane graph in which the common boundary of adjacent faces is a simple curve is 1-cycle resonant if and only if the outer face of G is alternating and each inner vertex has degree two. This extends a result from [X. Guo, F. Zhang, k-cycle resonant graphs, Discrete Math. 135 (1994) 113-120] that a hexagonal system is 1-cycle resonant if and only if it is...