{'fraction_non_alphanumeric': 0.018223234624145785, 'fraction_numerical': 0.009111617312072893, 'mean_word_length': 4.301204819277109, '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}}
Bounds on the leaf number in graphs of girth 4 or 5

Abstract Here, we prove new asymptotically sharp lower bounds on the leaf number in graphs of girth at least 4 or 5. The results imply upper bounds on the diameter of the aforementioned classes of graphs. In addition, we apply the dead leaves method to produce a short, unified, alternate proof to one of the results by Bonsma. We consider simple graphs only unless otherwise specified.