AbstractLet D be a disc, and let X be a finite subset of points on the boundary of D. An essential part of the proof of the four colour theorem is the fact that many sets of 4-colourings of X do not arise from the proper 4-colourings of any graph drawn in D. In contrast to this, we show that every set of 3-colourings of X arises from the proper 3-colourings of some graph drawn in D
Reverse mathematics is primarily interested in what set existence axioms are necessary in a proof of...
In the first partial result toward Steinberg's now-disproved three coloring conjecture, Abbott and Z...
AbstractIn this paper, we mainly prove that planar graphs without 4-, 7- and 9-cycles are 3-colorabl...
A graph G is uniquely k-colourable if the chromatic number of G is k and G has only one k-colouring ...
M.Sc.Within the field of Graph Theory the many ways in which graphs can be coloured have received a ...
A recent lower bound on the number of edges in a k-critical n-vertex graph by Kostochka and Yancey y...
AbstractFor the vertices of a finite 4-colored planar graph, regular of degree three, certain orient...
Includes bibliographical references (page 43)The main purpose of this paper is to investigate the co...
AbstractA simple proof of Grünbaum's theorem on the 3-colourability of planar graphs having at most ...
It is well known that the problem of planar graph colorability is strictly related to the famous fou...
AbstractPlanar graphs without 3-cycles at distance less than 4 and without 5-cycles are proved to be...
A conjecture due to the fourth author states that every $d$-regular planar multigraph can be $d$-edg...
AbstractThe four-colour theorem, that every loopless planar graph admits a vertex-colouring with at ...
The famous four color theorem states that for all planar graphs, every vertex can be assigned one of...
AbstractThe 4-Colour Theorem has been proved in the late seventies (Appel and Haken, 1977; Appel et ...
Reverse mathematics is primarily interested in what set existence axioms are necessary in a proof of...
In the first partial result toward Steinberg's now-disproved three coloring conjecture, Abbott and Z...
AbstractIn this paper, we mainly prove that planar graphs without 4-, 7- and 9-cycles are 3-colorabl...
A graph G is uniquely k-colourable if the chromatic number of G is k and G has only one k-colouring ...
M.Sc.Within the field of Graph Theory the many ways in which graphs can be coloured have received a ...
A recent lower bound on the number of edges in a k-critical n-vertex graph by Kostochka and Yancey y...
AbstractFor the vertices of a finite 4-colored planar graph, regular of degree three, certain orient...
Includes bibliographical references (page 43)The main purpose of this paper is to investigate the co...
AbstractA simple proof of Grünbaum's theorem on the 3-colourability of planar graphs having at most ...
It is well known that the problem of planar graph colorability is strictly related to the famous fou...
AbstractPlanar graphs without 3-cycles at distance less than 4 and without 5-cycles are proved to be...
A conjecture due to the fourth author states that every $d$-regular planar multigraph can be $d$-edg...
AbstractThe four-colour theorem, that every loopless planar graph admits a vertex-colouring with at ...
The famous four color theorem states that for all planar graphs, every vertex can be assigned one of...
AbstractThe 4-Colour Theorem has been proved in the late seventies (Appel and Haken, 1977; Appel et ...
Reverse mathematics is primarily interested in what set existence axioms are necessary in a proof of...
In the first partial result toward Steinberg's now-disproved three coloring conjecture, Abbott and Z...
AbstractIn this paper, we mainly prove that planar graphs without 4-, 7- and 9-cycles are 3-colorabl...
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