Simple vertex ordering characterizations for graph search
نویسندگان
چکیده
Graph searching is fundamental. Many graph algorithms employ some mechanism for systematically visiting all vertices and edges of a given graph. After choosing some initial sequence of vertices, it is natural to choose as the next vertex to visit some vertex that is adjacent to a previously visited vertex whenever possible. This statement describes graph search in its most general setting. When selecting a next vertex to visit, there are typically many such vertices that may be chosen. Strategies such as breadth-first search (BFS) and depth-first search (DFS) can be employed to choose among these vertices. Other strategies also exist. In the 1970s, Rose, Tarjan and Lueker [7] introduced a variant of BFS for determining perfect elimination orderings of chordal graphs. Their lexicographic breadth-first search (LexBFS) has garnered much attention recently and has become an important algorithm used for recognition of various graph families, diameter approximation, and finding key structures in certain graph classes [3]. One key point about LexBFS, and one of the reasons for its usefulness, is that there is a very simple characteri-
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