Nonrepetitive colorings of graphs -- a survey.
Note on graphs colouring
In this paper, we show that the maximal number of minimal colourings of a graph with vertices and the chromatic number is equal to , and the single graph for which this bound is attained consists of a -clique and isolated vertices.
Note on Gy. Elekes's conjectures concerning unavoidable patterns in proper colorings.
Note on highly connected monochromatic subgraphs in 2-colored complete graphs.
Note on improper coloring of -planar graphs
A graph is called improperly -colorable if the vertex set can be partitioned into subsets such that the graph induced by the vertices of has maximum degree at most for all . In this paper, we mainly study the improper coloring of -planar graphs and show that -planar graphs with girth at least are -colorable.
Note on -chromatic graphs
In this paper we characterize -chromatic graphs without isolated vertices and connected -chromatic graphs having a minimal number of edges.
Note on partitions of planar graphs
Chartrand and Kronk in 1969 showed that there are planar graphs whose vertices cannot be partitioned into two parts inducing acyclic subgraphs. In this note we show that the same is true even in the case when one of the partition classes is required to be triangle-free only.
Note On The Game Colouring Number Of Powers Of Graphs
We generalize the methods of Esperet and Zhu [6] providing an upper bound for the game colouring number of squares of graphs to obtain upper bounds for the game colouring number of m-th powers of graphs, m ≥ 3, which rely on the maximum degree and the game colouring number of the underlying graph. Furthermore, we improve these bounds in case the underlying graph is a forest.
Note on Turán's graph
Note sur une application de la classification hiérarchique à la coloration des graphes
Notes on nonrepetitive graph colouring.
Nowhere-zero 3-flows in squares of graphs.
Nowhere-zero -flows of supergraphs.
Nowhere-zero modular edge-graceful graphs
For a connected graph G of order n ≥ 3, let f: E(G) → ℤₙ be an edge labeling of G. The vertex labeling f’: V(G) → ℤₙ induced by f is defined as , where the sum is computed in ℤₙ. If f’ is one-to-one, then f is called a modular edge-graceful labeling and G is a modular edge-graceful graph. A modular edge-graceful labeling f of G is nowhere-zero if f(e) ≠ 0 for all e ∈ E(G) and in this case, G is a nowhere-zero modular edge-graceful graph. It is shown that a connected graph G of order n ≥ 3 is nowhere-zero...
O perfektních a kvaziperfektních grafech
Observability of a graph
On 1-Factorability and Edge-Colorability of Cartesian Products of Graphs.
On -choosability of toroidal graphs without chordal 7-cycles and adjacent 4-cycles
A graph is called -choosable if for every list assignment satisfying for all , there is an -coloring of such that each vertex of has at most neighbors colored with the same color as itself. In this paper, it is proved that every toroidal graph without chordal 7-cycles and adjacent 4-cycles is -choosable.
On a four-colour theorem.
On a pair of functional equations of combinatorial interest.