Graph properties checkable in linear time in the number of vertices
Abstract
This paper originates from the observation that many classical NP graph problems, including some NP - complete problems, are actually class vertex NLIN, which collects the graph problems computable on a nondeterministic RAM in time O(n) where n is the number of vertices of the input graph G=(V,E), rather than its usual size V+E. It appears that this class is robust (it is defined by a natural restrictive computational device ; it is logically characterized by several simple fragments of existential device ; it is closed under various combinatorial operators, including some restrictions of transitive closure) and meaningful (it contains many natural NP problems : connectivity, hamitonicity, non-planarity, etc). Furthermore, the very restrictive definition of vertex NLIN seems to have beneficial effects on our ability to answer difficult questions about complexity lower bounds or separation between determinism and nondeterminism.
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