## 40 Citations

Coloring graphs with no even holes ≥ 6: the triangle-free case

- MathematicsArXiv
- 2015

It is proved that the class of graphs with no triangle and no induced cycle of even length at least 6 has bounded chromatic number and the existence of C_4 is allowed.

Coloring the hypergraph of maximal cliques of a graph with no long path

- MathematicsDiscret. Math.
- 2003

On the chromatic number of a family of odd hole free graphs

- MathematicsArXiv
- 2021

It is proved that for (odd hole, full house)-free graph G, χ(G) ≤ ω(G)+ 1, and the equality holds if and only if ω (G) = 3 and G has H as an induced subgraph.

Clique-coloring some classes of odd-hole-free graphs

- Mathematics
- 2006

We consider the problem of clique-coloring, that is coloring the vertices of a given graph such that no maximal clique of size at least 2 is monocolored. Whereas we do not know any odd-hole-free…

Vertex Colouring and Forbidden Subgraphs – A Survey

- MathematicsGraphs Comb.
- 2004

This work surveys results on vertex colourings of graphs defined in terms of forbidden induced subgraph conditions in order to obtain useful results from a graph coloring formulation of his problem.

Four NP-complete problems about generalizations of perfect graphs

- Mathematics
- 2017

We show that the following problems are NP-complete.
1. Can the vertex set of a graph be partitioned into two sets such that each set induces a perfect graph?
2. Is the difference between the…

Clique-Coloring Claw-Free Graphs

- MathematicsGraphs Comb.
- 2016

It is proved that a claw-free graph with maximum degree at most 7, except an odd cycle longer than 3, has a 2-clique-coloring by using the decomposition theorem of Chudnovsky and Seymour.

A χ-binding function for the class of { 3 K 1 , K 1 ∪ K 4 }-free graphs

- Mathematics
- 2011

We prove that the chromatic number of any {3K1,K1∪K4}-free graph is at most a factor 28/15 times its clique number. In order to prove this result we prove that any connected subcubic triangle-free…

## References

SHOWING 1-10 OF 12 REFERENCES

The strong perfect-graph conjecture is true for K1, 3-free graphs

- MathematicsJ. Comb. Theory, Ser. B
- 1976

Colouring graphs with prescribed induced cycle lengths

- MathematicsSODA '99
- 1999

The surprising result is obtained that there exists no linear ´-binding function for G I (3;4), the class of all graphs whose induced cycle lengths are 4 or 5.

On the NP-completeness of the k-colorability problem for triangle-free graphs

- MathematicsDiscret. Math.
- 1996

The Ramsey Number R(3, t) Has Order of Magnitude t2/log t

- MathematicsRandom Struct. Algorithms
- 1995

It is proved that R(3, t) is bounded below by (1 – o(1))t/2/log t times a positive constant, and it follows that R (3), the Ramsey number for positive integers s and t, has asymptotic order of magnitude t2/ log t.

Random graphs

- MathematicsZOR Methods Model. Oper. Res.
- 1989

I study random graphs as a probabilist dealing with some combinatorial structures, and my methods are probabilistic and based on analysis, using for example integration theory, functional analysis, martingales and stochastic integration.

Graph Coloring Problems

- Mathematics
- 1994

Planar Graphs. Graphs on Higher Surfaces. Degrees. Critical Graphs. The Conjectures of Hadwiger and Hajos. Sparse Graphs. Perfect Graphs. Geometric and Combinatorial Graphs. Algorithms.…

Colouring random graphs

- Mathematics, Computer ScienceMathematical Proceedings of the Cambridge Philosophical Society
- 1975

This work discusses some results concerned with the behaviour of colouring algorithms on large random graphs and investigates the role of noise in the choice of colours.