Finite graph exploration by a mobile agent
The paper considers the task of finite connected graph exploration by a mobile agent. The mobile agent moves along the graph, reads and changes marks of the graph elements, and explores the graph based on this information. A new algorithm for finite undirected graph exploration of time complexity O(n3), space complexity O(n2) and the upper estimate of the number of transitions along the edges made by the agent O(n3) is proposed. For the algorithm to work, the agent needs one color. The algorithm is based on depth-first traversal method.