| Abstract: | A vertex dominating path in a graph is a path P such that every vertex outside P has a neighbor on P. In 1988 H. Broersma 5] stated a result implying that every n‐vertex k‐connected graph G such that  contains a vertex dominating path. We provide a short, self‐contained proof of this result and further show that every n‐vertex k‐connected graph such that  contains a vertex dominating path of length at most  , where T is a minimum dominating set of vertices. An immediate corollary of this result is that every such graph contains a vertex dominating path with length bounded above by a logarithmic function of the order of the graph. To derive this result, we prove that every n‐vertex k‐connected graph with  contains a path of length at most  , through any set of T vertices where  . |
