Add to ORKGA facial unique-maximum coloring of a plane graph is a proper vertex coloring by natural numbers where on each face α the maximal color appears exactly once on the vertices of α. Fabrici and Göring [4] proved that six colors are enough for any plane graph and conjectured that four colors suffice. This conjecture is a strengthening of the Four Color theorem. Wendland [6] later decreased the upper bound from six to five. In this note, we disprove the conjecture by giving an infinite family of counterexamples. s we conclude that facial unique-maximum chromatic number of the sphere is five
AbstractA facial parity edge colouring of a connected bridgeless plane graph is such an edge colouri...
In this paper we introduce the concept of zig-zag facial total-coloring of plane graphs. We obtain l...
AbstractIn 1975, Melnikov conjectured that the edges and faces of each plane graph G may be colored ...
A facial unique-maximum coloring of a plane graph is a proper coloring of the vertices using positiv...
The Four Color Theorem asserts that the vertices of every plane graph can be properly colored with f...
AbstractA vertex coloring of a plane graph is ℓ-facial if every two distinct vertices joined by a fa...
International audienceA vertex coloring of a plane graph is ℓ-facial if every two distinct vertices ...
A unique-maximum k-coloring with respect to faces of a plane graph G is a coloring with colors 1, . ...
Plummer and Toft conjectured in 1987 that the vertices of every 3-connected plane graph with maximum...
AbstractLet G be a plane graph with maximum face size Δ∗. If all faces of G with size four or more a...
International audienceA plane graph is l-facially k-colourable if its vertices can be coloured with ...
AbstractIn an l-facial coloring, any two different vertices that lie on the same face and are at dis...
In this thesis, we focus on variants of the coloring problem on graphs. A coloring of a graph $G$ is...
The Four Color Theorem says that the faces (or vertices) of a plane graph may be colored with four c...
AbstractIt was conjectured by Kronk and Mitchem in 1973 that simple plane graphs of maximum degree Δ...
AbstractA facial parity edge colouring of a connected bridgeless plane graph is such an edge colouri...
In this paper we introduce the concept of zig-zag facial total-coloring of plane graphs. We obtain l...
AbstractIn 1975, Melnikov conjectured that the edges and faces of each plane graph G may be colored ...
A facial unique-maximum coloring of a plane graph is a proper coloring of the vertices using positiv...
The Four Color Theorem asserts that the vertices of every plane graph can be properly colored with f...
AbstractA vertex coloring of a plane graph is ℓ-facial if every two distinct vertices joined by a fa...
International audienceA vertex coloring of a plane graph is ℓ-facial if every two distinct vertices ...
A unique-maximum k-coloring with respect to faces of a plane graph G is a coloring with colors 1, . ...
Plummer and Toft conjectured in 1987 that the vertices of every 3-connected plane graph with maximum...
AbstractLet G be a plane graph with maximum face size Δ∗. If all faces of G with size four or more a...
International audienceA plane graph is l-facially k-colourable if its vertices can be coloured with ...
AbstractIn an l-facial coloring, any two different vertices that lie on the same face and are at dis...
In this thesis, we focus on variants of the coloring problem on graphs. A coloring of a graph $G$ is...
The Four Color Theorem says that the faces (or vertices) of a plane graph may be colored with four c...
AbstractIt was conjectured by Kronk and Mitchem in 1973 that simple plane graphs of maximum degree Δ...
AbstractA facial parity edge colouring of a connected bridgeless plane graph is such an edge colouri...
In this paper we introduce the concept of zig-zag facial total-coloring of plane graphs. We obtain l...
AbstractIn 1975, Melnikov conjectured that the edges and faces of each plane graph G may be colored ...