Corpus ID: 237940692

Vertebrate interval graphs

@article{Jiang2021VertebrateIG,
  title={Vertebrate interval graphs},
  author={Rain Jiang and Kai Jiang and Minghui Jiang},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.12140}
}
  • Rain Jiang, Kai Jiang, Minghui Jiang
  • Published 24 September 2021
  • Computer Science, Mathematics
  • ArXiv
A vertebrate interval graph is an interval graph in which the maximum size of a set of independent vertices equals the number of maximal cliques. For any fixed v ≥ 1, there is a polynomial-time algorithm for deciding whether a vertebrate interval graph admits a vertex partition into two induced subgraphs with claw number at most v. In particular, when v = 2, whether a vertebrate interval graph can be partitioned into two proper interval graphs can be decided in polynomial time. 

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References

SHOWING 1-10 OF 14 REFERENCES
Trivially perfect graphs
  • M. Golumbic
  • Computer Science, Mathematics
  • Discret. Math.
  • 1978
TLDR
The trivially perfect graphs are characterized as a proper subclass of the triangulated graphs (thus disproving a claim of Buneman 3), and they are related to some well-known classes of perfect graphs. Expand
Partitioning an interval graph into subgraphs with small claws
  • Rain Jiang, Kai Jiang, Minghui Jiang
  • Computer Science, Mathematics
  • ArXiv
  • 2021
TLDR
A simple approximation algorithm for partitioning an interval graph into the minimum number of induced subgraphs with claw number at most v is presented, with approximation ratio 3 when 1 ≤ v ≤ 2, and 2 when v ≥ 3. Expand
The subchromatic number of a graph
The subchromatic number X S ( G ) of a graph G = ( V, E ) is the smallest order k of a partition {V 1 , V 2 , …, V k } of the vertices V ( G ) such that the subgraph ( V i ) induced by each subset VExpand
More About Subcolorings
TLDR
A number of results on the combinatorics, the algorithmics, and the complexity of subcolorings are derived, including asymptotically best possible upper bounds on the subchromatic number of interval graphs, chordal graphs, and permutation graphs in terms of the number of vertices. Expand
The complexity of G-free colourability
TLDR
It is shown that for any graph G on more than two vertices the problem is NP-complete, equivalent to having a bipartition of the vertex set where each cell is K2-free. Expand
Cubicity of Interval Graphs and the Claw Number
TLDR
This paper shows that for an interval graph G, cub ( G ) ⩽ ⌈ log 2 α ⌉ , where α is the independence number of G, and defines claw number ψ ( G) to be the largest positive integer m such that S ( m ) is an induced subgraph of G. Expand
Vertex-Partitioning into Fixed Additive Induced-Hereditary Properties is NP-hard
TLDR
If ${cal P} and ${\cal Q}$ are additive induced-hereditary graph properties, then $({\cal P}, {\cal Q})$-colouring is NP-hard, with the sole exception of graph $2$- Colouring (the case where both P and Q are the set of finite edgeless graphs). Expand
A short proof that 'proper = unit'
Abstract A short proof is given that the graphs with proper interval representations are the same as the graphs with unit interval representations.
Algorithmic graph theory and perfect graphs
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