Graph Coloring Problems

@inproceedings{Jensen1994GraphCP,
  title={Graph Coloring Problems},
  author={Tommy R. Jensen and Bjarne Toft},
  year={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. Constructions. Edge Colorings. Orientations and Flows. Chromatic Polynomials. Hypergraphs. Infinite Chromatic Graphs. Miscellaneous Problems. Indexes. 
On Coloring of Sparse Graphs
TLDR
The goal of this paper is to survey recent results of the authors on coloring and improper coloring of sparse graphs and to point out some polynomial-time algorithms for coloring (not necessarily optimal) of graphs with bounded maximum average degree. Expand
Some Conjectures and Questions in Chromatic Topological Graph Theory
We present a conjecture and eight open questions in areas of coloring graphs on the plane, on nonplanar surfaces, and on multiple planes. These unsolved problems relate to classical graph coloringExpand
Star Coloring and Acyclic Coloring of Locally Planar Graphs
It is proved that every graph embedded in a fixed surface with sufficiently large edge-width is acyclically 7-colorable and that its star chromatic number is at most $2s_0^*+3$, where $s_0^*\leq20$Expand
List VEF Coloring of Planar Graphs
In this paper the new coloring of planar, VEF-coloring, will be introduced. A VEF coloring of a simple planar graph G is a proper coloring of all elements, including vertices, edges and faces of G.Expand
Edge coloring regular graphs of high degree
TLDR
It is shown that the conjecture that if G = ( V, E ) is a Δ-regular simple graph with an even number of vertices at most 2Δ then G is Δ edge colorable is true for large graphs if | V | e ) Δ. Expand
Total colorings of planar graphs with large maximum degree
It is proved that a planar graph with maximum degree Δ ≥ 11 has total (vertex-edge) chromatic number $Delta; + 1. © 1997 John Wiley & Sons, Inc. J Graph Theory 26: 53–59, 1997
A Note on Graph Colorings and Graph Polynomials
It is known that the chromatic number of a graphG=(V,E) withV={1, 2, ?, n} exceedskiff the graph polynomialfG=?ij?E, i
( 5 , 2 )-Coloring of Sparse Graphs
We prove that every triangle-free graph whose subgraphs all have average degree less than 12/5 has a (5, 2)-coloring. This includes planar and projective-planar graphs with girth at least 12. Also,Expand
4-edge-coloring Graphs of Maximum Degree 3 in Linear Time
TLDR
A linear time algorithm is presented to properly color the edges of any graph of maximum degree 3 using 4 colors using a greedy approach and utilizes a new structure theorem for such graphs. Expand
Precise Upper Bound for the Strong Edge Chromatic Number of Sparse Planar Graphs
Abstract We prove that every planar graph with maximum degree ∆ is strong edge (2∆−1)-colorable if its girth is at least 40+1. The bound 2∆−1 is reached at any graph that has two adjacent vertices ofExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 1,061 REFERENCES
Coloring Planar Graphs in Parallel
TLDR
The vertex coloring algorithm 5 colors any planar graph, and the edge coloring algorithm Δ edge colors planar graphs with Δ ≥ 23 (and Δ + 1 edge colorsplanar graph with Δ) colors anyPlanar graphs. Expand
Edge coloring planar graphs with two outerplanar subgraphs
TLDR
This work gives a polynomial-time algorithm that edge colors any planar graph with two outerplanar subgraphs, which is clearly minimal for the class of planar graphs. Expand
Critical perfect graphs and perfect 3-chromatic graphs
  • A. Tucker
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. B
  • 1977
TLDR
It is proved that Berge's Strong Perfect Graph Conjecture is valid for 3-chromatic graphs and not just for perfect graphs based on Fulkerson's antiblocking polyhedra approach to perfect graphs. Expand
On Linear-Time Algorithms for Five-Coloring Planar Graphs
TLDR
These properties assure good performance in two linear-time algorithms for five-coloring planar graphs, and a newlinear-time algorithm, based on a third property, is presented. Expand
Total Colourings of Graphs
Basic terminology and introduction.- Some basic results.- Complete r-partite graphs.- Graphs of low degree.- Graphs of high degree.- Classification of type 1 and type 2 graphs.- Total chromaticExpand
On the edge-chromatic number of a graph
TLDR
Various ways of constructing graphs whose edge-chromatic number is @r + 1 and a conjecture about such graphs are described and formulated. Expand
Clique covers and coloring problems of graphs
  • W. Klotz
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. B
  • 1989
TLDR
Using clique covers these theorems can be turned into statements on the chromatic number of a graph and covering and coloring problems suggested by these versions of the theorem are investigated. Expand
Subgraphs of colour-critical graphs
TLDR
In section 3 arbitrarily largek-critical graphs withn vertices are constructed such that, in order to reduce the chromatic number tok−2, at leastckn2 edges must be removed. Expand
Hajós' graph-coloring conjecture: Variations and counterexamples
  • P. A. Catlin
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. B
  • 1979
TLDR
It is shown that a graph with chromatic number 4 contains as a subgraph a subdivided K4 in which each triangle of the K4 is subdivided to form an odd cycle. Expand
A Linear 5-Coloring Algorithm of Planar Graphs
A simple linear algorithm is presented for coloring planar graphs with at most five colors. The algorithm employs a recursive reduction of a graph involving the deletion of a vertex of degree 6 orExpand
...
1
2
3
4
5
...