This paper presents a method to segment single- and multiple-touching characters in offline handwritten Japanese text recognition with practical speed. Distortions due to handwriting and a mix of complex Chinese characters with simple phonetic and alphanumeric characters leave optical handwritten text recognition (OHTR) for Japanese still far from perfection. Segmentation of characters, which touch neighbors on multiple points, is a serious unsolved problem. Therefore, we propose a method to segment them which is made in two steps: coarse segmentation and fine segmentation. The coarse segmentation employs vertical projection, stroke-width estimation while the fine segmentation takes a graph-based approach for thinned text images, which employs a new bridge finding process and Voronoi diagrams with two improvements. Unlike previous methods, it locates character centers and seeks segmentation candidates between them. It draws vertical lines explicitly at estimated character centers in order to prevent vertically unconnected components from being left behind in the bridge finding. Multiple candidates of separation are produced by removing touching points combinatorially. SVM is applied to discard improbable segmentation boundaries. Then, ambiguities are finally solved by the text recognition employing linguistic context and geometric context to recognize segmented characters. The results of our experiments show that the proposed method can segment not only single-touching characters but also multiple-touching characters, and each component in our proposed method contributes to the improvement of segmentation and recognition rates.