Bibliographic Details
| Title: |
Characterizing path-factor uniform graphs with respect to the degree sum of non-adjacent vertices. |
| Authors: |
Zhang, Ping1 (AUTHOR) mathzhangping@126.com |
| Source: |
RAIRO: Operations Research (2804-7303). 2025, Vol. 59 Issue 6, p3675-3681. 7p. |
| Subjects: |
Graph theory, Subgraphs |
| Abstract: |
For a graph G and a set H of connected graphs, an H-factor of G is a spanning subgraph of G with each component isomorphic to some member in H. If each component of H is isomorphic to a path, then we call the H-factor a path-factor. For each integer k ≥ 2, a graph G is P≥k-factor uniform if for any two distinct edges e1 and e2, G admits a P≥k-factor including e1 and excluding e2. In this note, we determine two lower bounds on the degree sum of non-adjacent vertices to ensure that G is P≥k-factor uniform for k = 2 and k = 3. Furthermore, we construct some extremal graphs to show that the bounds are best possible. The results improve some known results slightly. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
