Standard DFS and BFS suffice to recognize and certify trivially perfect graphs, split graphs, bipartite chain graphs, and proper interval graphs using pattern-avoiding vertex orderings.
Discrete Mathematics24(1), 105–107 (1978)
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On the power of standard DFS and BFS
Standard DFS and BFS suffice to recognize and certify trivially perfect graphs, split graphs, bipartite chain graphs, and proper interval graphs using pattern-avoiding vertex orderings.