Spanning path-cycle systems with given end-vertices in regular graphs (full version)
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911106153316352 |
|---|---|
| author | Egawa, Yoshimi Kano, Mikio Ozeki, Kenta |
| author_facet | Egawa, Yoshimi Kano, Mikio Ozeki, Kenta |
| contents | We prove the following theorem. Let $r\ge 4$ be an integer, and $G$ be a $K_{1,r}$-free $r$-edge-connected $r$-regular graph. Then, for every set $W$ of even number of vertices of $G$ such that the distance between any two vertices of $W$ in $G$ is at least 3, $G$ has vertex-disjoint paths and cycles $P_1, \ldots, P_m, C_1, \ldots, C_n$ such that (i) $V(G)=V(P_1) \cup \cdots \cup V(P_m) \cup V(C_1) \cup \cdots \cup V(C_n)$, (ii) each path $P_i$ connects two vertices of $W$, and (iii) the set of the end-vertices of $P_i$'s is equal to $W$. A similar result for a 3-regular graph is obtained in [Graphs Combin. {\bf 39} (2023) \#85]. However, our proof is widely different from its proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11302 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spanning path-cycle systems with given end-vertices in regular graphs (full version) Egawa, Yoshimi Kano, Mikio Ozeki, Kenta Combinatorics We prove the following theorem. Let $r\ge 4$ be an integer, and $G$ be a $K_{1,r}$-free $r$-edge-connected $r$-regular graph. Then, for every set $W$ of even number of vertices of $G$ such that the distance between any two vertices of $W$ in $G$ is at least 3, $G$ has vertex-disjoint paths and cycles $P_1, \ldots, P_m, C_1, \ldots, C_n$ such that (i) $V(G)=V(P_1) \cup \cdots \cup V(P_m) \cup V(C_1) \cup \cdots \cup V(C_n)$, (ii) each path $P_i$ connects two vertices of $W$, and (iii) the set of the end-vertices of $P_i$'s is equal to $W$. A similar result for a 3-regular graph is obtained in [Graphs Combin. {\bf 39} (2023) \#85]. However, our proof is widely different from its proof. |
| title | Spanning path-cycle systems with given end-vertices in regular graphs (full version) |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.11302 |