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Net."],"published-print":{"date-parts":[[2026,6]]},"abstract":"<jats:p>For a set [Formula: see text] of connected graphs, a spanning subgraph [Formula: see text] of a graph [Formula: see text] is called an [Formula: see text]-factor if each component of [Formula: see text] is isomorphic to a member of [Formula: see text]. In this paper, we obtain a sufficient condition with regard to tight toughness, isolated toughness and binding number bounds to guarantee the existence of a [Formula: see text]-factor, two sufficient conditions to guarantee the existence of a [Formula: see text]-factor in a bipartite graph and some sufficient conditions for [Formula: see text]-factor deleted graph and a [Formula: see text]-factor deleted graph.<\/jats:p>","DOI":"10.1142\/s0219265925500069","type":"journal-article","created":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T01:02:08Z","timestamp":1742605328000},"source":"Crossref","is-referenced-by-count":0,"title":["Tight Toughness, Isolated Toughness and Binding Number Bounds for Some Factors and Some Factor-Deleted Graphs"],"prefix":"10.1142","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-7085-9824","authenticated-orcid":false,"given":"Run","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Qinghai Normal University, Xining 810001, P. 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