We give algorithms for the directed minimum odd or even cut problem and certain generalizations. Our algorithms improve on the previous best ones of Goemans and Ramakrishnan by a factor of O(n) (here n is the size of the ground vertex set). Our improvements apply among others to the minimum directed Todd or T-even cut and to the directed minimum Steiner cut problems. The (slightly more general)...

a dominating set $d subseteq v$ of a graph $g = (v,e)$ is said to be a connected cototal dominating set if $langle d rangle$ is connected and $langle v-d rangle neq phi$, contains no isolated vertices. a connected cototal dominating set is said to be minimal if no proper subset of $d$ is connected cototal dominating set. the connected cototal domination number $gamma_{ccl}(g)$ of $g$ is the min...

Let an edge cut partition the vertex set of a graph into k disjoint subsets A1, . . . , Ak with ||Ai| − |Aj || ≤ 1. We consider the problem of determining the minimal size of such a cut for a given graph. For this we introduce a new lower bound method which is based on the solution of an extremal set problem and present bounds for some graph classes based on Hamming graphs.