AbstractEvery graph embedded on a surface of positive genus with every face bounded by an even number of edges can be 3-colored provided all noncontractible cycles in the graph are sufficiently long. The bound of three colors is the smallest possible for this type of result
In the first partial result toward Steinberg's now-disproved three coloring conjecture, Abbott and Z...
Let G be a plane graph of girth at least five. We show that if there exists a 3-coloring of a cycle ...
AbstractA simple proof of Grünbaum's theorem on the 3-colourability of planar graphs having at most ...
AbstractEvery graph embedded on a surface of positive genus with every face bounded by an even numbe...
In this article, we show that there exists an integer k(Sigma) greater than or equal to 5 such that,...
The Four Color Theorem is equivalent with its dual form stating that each 2-edge-connected 3-regular...
AbstractPlanar graphs without cycles of length from 4 to 7 are proved to be 3-colorable. Moreover, i...
AbstractA polyhedral embedding in a surface is one in which any two faces have boundaries that are e...
Let G be a plane graph with exactly one triangle T and all other cycles of length at least 5, and le...
AbstractIt is shown that there is a constant c such that if G is a graph embedded in a surface of ge...
AbstractIn 1976, Steinberg conjectured that plane graphs without cycles of length 4 and 5 are 3-colo...
A total-k-coloring of a graph G is a coloring of V ∪ E using k colors such that no two adjacent or i...
AbstractThe face hypergraph of a graph G embedded on a surface has the same vertex set as G and its ...
We show in this paper that in every 3-coloring of the edges of Kn all but o(n) of its vertices can b...
AbstractIt is proved that there is a function f:N→N such that the following holds. Let G be a graph ...
In the first partial result toward Steinberg's now-disproved three coloring conjecture, Abbott and Z...
Let G be a plane graph of girth at least five. We show that if there exists a 3-coloring of a cycle ...
AbstractA simple proof of Grünbaum's theorem on the 3-colourability of planar graphs having at most ...
AbstractEvery graph embedded on a surface of positive genus with every face bounded by an even numbe...
In this article, we show that there exists an integer k(Sigma) greater than or equal to 5 such that,...
The Four Color Theorem is equivalent with its dual form stating that each 2-edge-connected 3-regular...
AbstractPlanar graphs without cycles of length from 4 to 7 are proved to be 3-colorable. Moreover, i...
AbstractA polyhedral embedding in a surface is one in which any two faces have boundaries that are e...
Let G be a plane graph with exactly one triangle T and all other cycles of length at least 5, and le...
AbstractIt is shown that there is a constant c such that if G is a graph embedded in a surface of ge...
AbstractIn 1976, Steinberg conjectured that plane graphs without cycles of length 4 and 5 are 3-colo...
A total-k-coloring of a graph G is a coloring of V ∪ E using k colors such that no two adjacent or i...
AbstractThe face hypergraph of a graph G embedded on a surface has the same vertex set as G and its ...
We show in this paper that in every 3-coloring of the edges of Kn all but o(n) of its vertices can b...
AbstractIt is proved that there is a function f:N→N such that the following holds. Let G be a graph ...
In the first partial result toward Steinberg's now-disproved three coloring conjecture, Abbott and Z...
Let G be a plane graph of girth at least five. We show that if there exists a 3-coloring of a cycle ...
AbstractA simple proof of Grünbaum's theorem on the 3-colourability of planar graphs having at most ...
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