Two-cacti with minimum number of spanning trees

AbstractZelinka (1978) proved that the spanning trees of a 2-cactus partition into at least 3 isomorphism classes. Here we examine the structure of these 2-cacti for which the spanning trees partition into exactly 3 isomorphism classes

Spanning trees in a cactus

AbstractWe prove a best possible lower bound for the number of isomorphism classes into which all rooted spanning trees of a rooted cactus partition. We announce a best possible lower bound for the number of isomorphism classes into which all spanning trees of a cactus partition

Even [a,b]-factors in graphs

Let a and b be integers 4 ≤ a ≤ b. We give simple, sufficient conditions for graphs to contain an even [a,b]-factor. The conditions are on the order and on the minimum degree, or on the edge-connectivity of the graph