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This is a Quantitative Study study.

September 30, 2025Open Access

Some sufficient conditions for graphs to have component factors

Key Points

Sufficient conditions for k-factors in graphs were identified, enhancing understanding in graph theory.
The results reveal that certain extremal graphs demonstrate the best possible scenarios for these factors.
The study focuses on spanning subgraphs whose components align with specific graph families.
These findings contribute to the broader discussion on the structure and properties of graphs.

Abstract

Let G denote a graph and k2 be an integer. A \K₁, ₁, K₁, ₂, , K₁, ₊, T (2k+1) \-factor of G is a spanning subgraph, whose every connected component is isomorphic to an element of \K₁, ₁, K₁, ₂, , K₁, ₊, T (2k+1) \, where T (2k+1) is one special family of tree. In this paper, we put forward some sufficient conditions for the existence of \K₁, ₁, K₁, ₂, , K₁, ₊, T (2k+1) \-factors in graphs. Furthermore, we construct some extremal graphs to show that the main results in this paper are best possible.

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Cite This Study

Sizhong Zhou (Fri,) studied this question.

synapsesocial.com/papers/68dc1e358a7d58c25ebb192b https://doi.org/https://doi.org/10.1051/ro/2025127