Parallel programming/execution frameworks for many/multi-core platforms should support as many applications as possible. In general, work-stealing frameworks provide efficient load balancing even for irregular parallel applications. Unfortunately, naïve parallel programs which traverse graph-based data structures (e.g., for constructing spanning trees) cause stack overflow or unacceptable load imbalance. In this study, we develop parallel programs to perform probabilistically balanced divide-and-conquer graph traversals. We propose a programming technique for accumulating overflowed calls for the next iteration of repeated parallel stages. In an emerging backtracking-based work-stealing framework called “Tascell, ” which features on-demand concurrency, we propose a programming technique for long-term exclusive use of workspaces, leading to a similar technique also in the Cilk framework.