# 3-consecutive C-colorings of graphs

@article{Bujts20103consecutiveCO, title={3-consecutive C-colorings of graphs}, author={Csilla Bujt{\'a}s and Charles Dominic and E. Sampathkumar and M. S. Subramanya and Zsolt Tuza}, journal={Discuss. Math. Graph Theory}, year={2010}, volume={30}, pages={393-405} }

A 3-consecutive C-coloring of a graph G = (V;E) is a mapping ’ : V !N such that every path on three vertices has at most two colors. We prove general estimates on the maximum number „ ´3CC(G) of colors in a 3-consecutive C-coloring of G, and characterize the structure of connected graphs with „ ´3CC(G) ‚ k for k = 3 and k = 4.

## 17 Citations

### Vertex Colorings without Rainbow Subgraphs

- MathematicsDiscuss. Math. Graph Theory
- 2016

The F-upper chromatic number of G is defined as the maximum number of colors that can be used to color the vertices of G such that there is no rainbow copy of F such that its vertices receive distinct colors.

### When the vertex coloring of a graph is an edge coloring of its line graph - a rare coincidence

- MathematicsArs Comb.
- 2016

For graphs G of minimum degree at least 2, denoting by L(G) the line graph of G, it is proved that there is a bijection between the 3-consecutive vertex colorings of G and the3- Consecutive edge coloring of L, which keeps the number of colors unchanged, too.

### Worm Colorings

- MathematicsDiscuss. Math. Graph Theory
- 2015

This work defines an F-WORM coloring of G as a coloring of the vertices of G without a rainbow or monochromatic subgraph H isomorphic to F, and presents some results on this concept especially as regards to the existence, complexity, and optimization within certain graph classes.

### Vertex Colorings without Rainbow or Monochromatic Subgraphs

- Mathematics
- 2016

This paper investigates vertex colorings of graphs such that some rainbow subgraph~$R$ and some monochromatic subgraph $M$ are forbidden. Previous work focussed on the case that $R=M$. Here we…

### Coloring subgraphs with restricted amounts of hues

- Mathematics
- 2017

Abstract We consider vertex colorings where the number of colors given to specified subgraphs is restricted. In particular, given some fixed graph F and some fixed set A of positive integers, we…

### WORM Colorings of Planar Graphs

- MathematicsDiscuss. Math. Graph Theory
- 2017

It is proved that any 3-connected plane graph (respectively outerplane graph) admits a 2-coloring such that no facial path on five (respective four) vertices is monochromatic.

### K3-Worm Colorings of Graphs: Lower Chromatic Number and Gaps in the Chromatic Spectrum

- MathematicsDiscuss. Math. Graph Theory
- 2016

It is proved that it is NP-hard to determine the minimum number of colors, and NP-complete to decide k-colorability for every k ≥ 2 (and remains intractable even for graphs of maximum degree 9 if k = 3), and positive results for d-degenerate graphs with small d are proved.

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