Bibliographic Details
| Title: |
The spanning 3-connectivity of circuit graphs of matroids. |
| Authors: |
Li, Wen1 (AUTHOR) Lwxju1123@163.com, Xiong, Wei1 (AUTHOR) xingheng-1985@163.com, Wang, Xiaoqian1 (AUTHOR) wxq18563352519@sina.com, Lai, Hong-Jian2,3 (AUTHOR) hjlai2015@hotmail.com |
| Source: |
Discrete Applied Mathematics. Jul2026, Vol. 388, p108-115. 8p. |
| Subjects: |
Matroids, Graph connectivity, Hamiltonian graph theory, Graph theory |
| Abstract: |
A graph G is spanning k -connected if for any two vertices u , v ∈ V (G) and for all integers s with 0 ≤ s ≤ k , G has a subgraph H consisting of s -internally disjoint (u , v) -paths such that V (H) = V (G). Thus, if G is spanning 1-connected, it implies that G is Hamilton-connected. The circuit graph of a matroid M is a simple graph G (M) which has vertex set V (G) = C (M) , the collection of all circuits of M , and edge set E (G) = { C C ′ | C , C ′ ∈ C (M) , | C ∩ C ′ | ≠ 0 }. We prove that every circuit graph of a connected matroid containing at least 4 circuits is spanning 3-connected. This result extends a former result on Hamilton-connectedness of circuit graph of matroids in Li and Liu (2008). [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
