@article{oai:kyutech.repo.nii.ac.jp:00007780,
 author = {Eto, Hiroshi and Kawahara, Hiroyuki and Miyano, Eiji and 宮野, 英次 and Nonoue, Natsuki},
 issue = {3},
 journal = {IEICE Transactions on Information and Systems},
 month = {Mar},
 note = {In this paper, we study a variant of the Minimum Dominating Set problem. Given an unweighted undirected graph G=(V,E) of n=|V| vertices, the goal of the Minimum Single Dominating Cycle problem (MinSDC) is to find a single shortest cycle which dominates all vertices, i.e., a cycle C such that for the set V(C) of vertices in C and the set N(V(C)) of neighbor vertices of C, V(G)=V(C)∪N(V(C)) and |V(C)| is minimum over all dominating cycles in G [6], [17], [24]. In this paper we consider the (in)approximability of MinSDC if input graphs are restricted to some special classes of graphs. We first show that MinSDC is still NP-hard to approximate even when restricted to planar, bipartite, chordal, or r-regular (r≥3). Then, we show the (lnn+1)-approximability and the (1-ε)lnn-inapproximability of MinSDC on split graphs under P≠NP. Furthermore, we explicitly design a linear-time algorithm to solve MinSDC for graphs with bounded treewidth and estimate the hidden constant factor of its running time-bound.},
 pages = {574--581},
 title = {Complexity of the Minimum Single Dominating Cycle Problem for Graph Classes},
 volume = {E101.D},
 year = {2018},
 yomi = {ミヤノ, エイジ}
}