  We study the problem of online graph exploration on undirected graphs, where
a searcher has to visit every vertex and return to the origin. Once a new
vertex is visited, the searcher learns of all neighboring vertices and the
connecting edge weights. The goal such an exploration is to minimize its total
cost, where each edge traversal incurs a cost of the corresponding edge weight.
We investigate the problem on tadpole graphs (also known as dragons, kites),
which consist of a cycle with an attached path. Miyazaki et al. (The online
graph exploration problem on restricted graphs, IEICE Transactions 92-D (9),
2009) showed that every online algorithm on these graphs must have a
competitive ratio of 2-epsilon, but did not provide upper bounds for non-unit
edge weights. We show via amortized analysis that a greedy approach yields a
matching competitive ratio of 2 on tadpole graphs, for arbitrary non-negative
edge weights.
