Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.18090 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914211912744960 |
|---|---|
| author | Xiao, Benjamin Ye, Dong |
| author_facet | Xiao, Benjamin Ye, Dong |
| contents | Let $G$ be a graph and $S$ be a set of cliques of $G$. The set $S$ is an indeque set if every component of $G[S]$, the subgraph induced by vertices of $S$, is a clique. In this paper, we prove that the indeque ratio of $K_4$-minor-free graphs is $\frac 1 2$, which settle two conjectures of Biro, Collado and Zamora. We also show that the indeque ratio of subcubic graphs is $\frac 1 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18090 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Packing Independent Cliques in $K_4$-minor-free Graphs Xiao, Benjamin Ye, Dong Combinatorics 05C69 Let $G$ be a graph and $S$ be a set of cliques of $G$. The set $S$ is an indeque set if every component of $G[S]$, the subgraph induced by vertices of $S$, is a clique. In this paper, we prove that the indeque ratio of $K_4$-minor-free graphs is $\frac 1 2$, which settle two conjectures of Biro, Collado and Zamora. We also show that the indeque ratio of subcubic graphs is $\frac 1 2$. |
| title | Packing Independent Cliques in $K_4$-minor-free Graphs |
| topic | Combinatorics 05C69 |
| url | https://arxiv.org/abs/2512.18090 |