AbstractFor every surface S there exists a natural number n(S) such that every map drawn on S can be colored using live colors only provided every simple noncontractible closed curve on the surface contains at least n(S) border points of the map. This proves a conjecture of M. O. Albertson and W. R. Stromquist. There is no four-color theorem of this type
In this note, we show that the edges and faces of any plane graph with maximum degree three can be s...
AbstractRingel has shown that the set of vertices and regions of any normal map on the sphere can be...
International audienceWe answer in the negative a question of Oporowski and Zhao [Discrete Math., 30...
The four-colour conjecture (4CC) is a question that asks whether any map can be coloured using only ...
Includes bibliographical references (page 43)The main purpose of this paper is to investigate the co...
Thomassen proved that there are only finitely many 6-critical graphs embeddable on a fixed surface. ...
AbstractA triangulation is said to be even if each vertex has even degree. It is known that every ev...
very planar map of connected countries can be colored using four colors in such a way that countries...
AbstractWe prove a color extension result implying that, for every fixed surface S, there are only f...
Certainly any mathematical theorem concerning the coloring of maps would be relevant and widely appl...
In this note, we show that the edges and faces of any plane graph with maximum degree three can be s...
The Four-Color Theorem originated from the attempt to solve the problem of painting MAPS over a plan...
As stated originally the four – color problem asked whether it is always possible to color the regio...
AbstractWe prove that, for every fixed surface S, there exists a largest positive constant c such th...
AbstractA generalization of the idea of a coloring is proposed in which regions of a map may be assi...
In this note, we show that the edges and faces of any plane graph with maximum degree three can be s...
AbstractRingel has shown that the set of vertices and regions of any normal map on the sphere can be...
International audienceWe answer in the negative a question of Oporowski and Zhao [Discrete Math., 30...
The four-colour conjecture (4CC) is a question that asks whether any map can be coloured using only ...
Includes bibliographical references (page 43)The main purpose of this paper is to investigate the co...
Thomassen proved that there are only finitely many 6-critical graphs embeddable on a fixed surface. ...
AbstractA triangulation is said to be even if each vertex has even degree. It is known that every ev...
very planar map of connected countries can be colored using four colors in such a way that countries...
AbstractWe prove a color extension result implying that, for every fixed surface S, there are only f...
Certainly any mathematical theorem concerning the coloring of maps would be relevant and widely appl...
In this note, we show that the edges and faces of any plane graph with maximum degree three can be s...
The Four-Color Theorem originated from the attempt to solve the problem of painting MAPS over a plan...
As stated originally the four – color problem asked whether it is always possible to color the regio...
AbstractWe prove that, for every fixed surface S, there exists a largest positive constant c such th...
AbstractA generalization of the idea of a coloring is proposed in which regions of a map may be assi...
In this note, we show that the edges and faces of any plane graph with maximum degree three can be s...
AbstractRingel has shown that the set of vertices and regions of any normal map on the sphere can be...
International audienceWe answer in the negative a question of Oporowski and Zhao [Discrete Math., 30...
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