@techreport{oai:ipsj.ixsq.nii.ac.jp:00217353,
 author = {Yasuaki, Kobayashi and Shunsuke, Nagano and Yota, Otachi and Yasuaki, Kobayashi and Shunsuke, Nagano and Yota, Otachi},
 issue = {5},
 month = {Mar},
 note = {For a connected graph G = (V, E) and s, t ∈ V, a non-separating s-t path is a path P between s and t such that the set of vertices of P does not separate G, that is, G - V (P) is connected. An s-t path is non-disconnected if G - E(P) is connected. The problems of finding shortest non-separating and non-disconnecting paths are both known to be NP-hard. In this paper, we consider the problems from the viewpoint of parameterized complexity. We show that the problem of finding a non-separating s-t path of length at most k is W[1]-hard parameterized by k, while the non-disconnecting counterpart is fixed-parameter tractable parameterized by k. We also consider the shortest non-separating path problem on several classes of graphs and show that this problem is NP-hard even on bipartite graphs, chordal graphs, and planar graphs. As for positive results, the shortest non-separating path problem is fixed-parameter tractable parameterized by k on planar graphs and polynomial-time solvable on chordal graphs if k is the shortest path distance between s and t., For a connected graph G = (V, E) and s, t ∈ V, a non-separating s-t path is a path P between s and t such that the set of vertices of P does not separate G, that is, G - V (P) is connected. An s-t path is non-disconnected if G - E(P) is connected. The problems of finding shortest non-separating and non-disconnecting paths are both known to be NP-hard. In this paper, we consider the problems from the viewpoint of parameterized complexity. We show that the problem of finding a non-separating s-t path of length at most k is W[1]-hard parameterized by k, while the non-disconnecting counterpart is fixed-parameter tractable parameterized by k. We also consider the shortest non-separating path problem on several classes of graphs and show that this problem is NP-hard even on bipartite graphs, chordal graphs, and planar graphs. As for positive results, the shortest non-separating path problem is fixed-parameter tractable parameterized by k on planar graphs and polynomial-time solvable on chordal graphs if k is the shortest path distance between s and t.},
 title = {Finding shortest non-separating and non-disconnecting paths},
 year = {2022}
}