# Disjoint Triangles of a Cubic Line Graph

@article{Zhang2004DisjointTO, title={Disjoint Triangles of a Cubic Line Graph}, author={Xiaodong Zhang and Stanislaw Bylka}, journal={Graphs and Combinatorics}, year={2004}, volume={20}, pages={275-280} }

Abstract.In this paper, we prove that a cubic line graph G on n vertices rather than the complete graph K4 has vertex-disjoint triangles and the vertex independence number . Moreover, the equitable chromatic number, acyclic chromatic number and bipartite density of G are respectively.

## 4 Citations

### Planarization and Acyclic Colorings of Subcubic Claw-Free Graphs

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- 2011

The largest known subclass of subcubic graphs such that an optimal acyclic vertex coloring can be found in polynomial-time is presented, and it is shown that this bound is tight by proving that the problem is NP-hard for cubic line graphs (and therefore, claw-free graphs) of maximum degree d≥4.

### A Complexity Picture for H-Free Graphs

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### Acyclic, Star and Injective Colouring: A Complexity Picture for H-Free Graphs

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- 2020

This study gives almost complete classifications for the computational complexity of Acyclic Colouring, Star Colouring and Injective Colouring for H-free graphs and concludes that for fixed k the three problems behave in the same way, but this is no longer true if k is part of the input.

### Counting Edge-injective Homomorphisms and Matchings on Restricted Graph Classes

- MathematicsTheory of Computing Systems
- 2018

It is shown that edge-injective homomorphisms from a pattern graph £H$ can be counted in polynomial time if $H$ has bounded vertex-cover number after removing isolated edges and if the graphs in $\mathcal{H}$ have unbounded vertex- cover number even after deleting isolated edges.

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