A simple path in a graph is a path that contains no repeated vertices, and (therefore) no cycles. Let G be an undirected graph and consider the languages: SPATH = { | G has a simple path of length | G...

A simple path in a graph is a path that contains no repeated vertices, and (therefore) no cycles. Let G be an<br>undirected graph and consider the languages:<br>SPATH = { <G, a, b, k> | G has a simple path of length <k from a to b}<br>LPATH = { <G, a, b, k> | G has a simple path of length > k from a to b}<br>a. Show that SPATH E P.<br>b. Show that LPATH is NP-complete.<br>

Extracted text: A simple path in a graph is a path that contains no repeated vertices, and (therefore) no cycles. Let G be an undirected graph and consider the languages: SPATH = { | G has a simple path of length | G has a simple path of length > k from a to b} a. Show that SPATH E P. b. Show that LPATH is NP-complete.

Jun 04, 2022

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A simple path in a graph is a path that contains no repeated vertices, and (therefore) no cycles. Let G be an undirected graph and consider the languages: SPATH = { | G has a simple path of length | G...

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