{'fraction_non_alphanumeric': 0.0397456279809221, 'fraction_numerical': 0.025437201907790145, 'mean_word_length': 4.338983050847458, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
On arc‐traceable tournaments

A digraph D = (V, A) is arc‐traceable if for each arc xy in A, xy lies on a directed path containing all the vertices of V, that is, a hamiltonian path. Given a tournament T, it is well known that it contains a directed hamiltonian path. In this article, we develop the structure necessary for a tournament T to contain an arc xy that is not on any hamiltonian path. Using this structure, we give sufficient conditions for a tournament to be arc‐traceable. In addition, we give examples to show that these conditions are best possible. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 157–166, 2006