AbstractAksinov and Mel'nikov conjectured that every edge-critical non-3-colorable planar graph with triangles at distance at least one has connectivity 2. By constructing 3-connected edge-critical non-3-colorable planar graphs in which the distance between triangles is 2 or more, this conjecture is refuted
AbstractIn this note, it is proved that every plane graph without 5- and 7-cycles and without adjace...
Aksenov proved that in a planar graph $G$ with at most one triangle, every precoloring of a 4-cycle ...
The Four Color Theorem is equivalent with its dual form stating that each 2-edge-connected 3-regular...
AbstractAksinov and Mel'nikov conjectured that every edge-critical non-3-colorable planar graph with...
A recent lower bound on the number of edges in a k-critical n-vertex graph by Kostochka and Yancey y...
A graph G is uniquely k-colourable if the chromatic number of G is k and G has only one k-colouring ...
Aksenov proved that in a planar graph G with at most one triangle, every precoloring of a 4-cycle ca...
By the Grünbaum-Aksenov Theorem (extending Grötzsch’s Theorem) every planar graph with at most thr...
AbstractIn this paper we construct some counterexamples of non-3-colorable planar graphs, using the ...
A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up...
AbstractPlanar graphs without 3-cycles at distance less than 4 and without 5-cycles are proved to be...
AbstractIn 1970, Havel asked if each planar graph with the minimum distance, d∇, between triangles l...
In the first partial result toward Steinberg's now-disproved three coloring conjecture, Abbott and Z...
AbstractThis short note provides a counterexample to a conjecture of Erdős on non-3-colorable planar...
First, let a graph be a set of vertices (points) and a set of edges (lines) connecting these vertice...
AbstractIn this note, it is proved that every plane graph without 5- and 7-cycles and without adjace...
Aksenov proved that in a planar graph $G$ with at most one triangle, every precoloring of a 4-cycle ...
The Four Color Theorem is equivalent with its dual form stating that each 2-edge-connected 3-regular...
AbstractAksinov and Mel'nikov conjectured that every edge-critical non-3-colorable planar graph with...
A recent lower bound on the number of edges in a k-critical n-vertex graph by Kostochka and Yancey y...
A graph G is uniquely k-colourable if the chromatic number of G is k and G has only one k-colouring ...
Aksenov proved that in a planar graph G with at most one triangle, every precoloring of a 4-cycle ca...
By the Grünbaum-Aksenov Theorem (extending Grötzsch’s Theorem) every planar graph with at most thr...
AbstractIn this paper we construct some counterexamples of non-3-colorable planar graphs, using the ...
A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up...
AbstractPlanar graphs without 3-cycles at distance less than 4 and without 5-cycles are proved to be...
AbstractIn 1970, Havel asked if each planar graph with the minimum distance, d∇, between triangles l...
In the first partial result toward Steinberg's now-disproved three coloring conjecture, Abbott and Z...
AbstractThis short note provides a counterexample to a conjecture of Erdős on non-3-colorable planar...
First, let a graph be a set of vertices (points) and a set of edges (lines) connecting these vertice...
AbstractIn this note, it is proved that every plane graph without 5- and 7-cycles and without adjace...
Aksenov proved that in a planar graph $G$ with at most one triangle, every precoloring of a 4-cycle ...
The Four Color Theorem is equivalent with its dual form stating that each 2-edge-connected 3-regular...
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