Add to ORKGBy the Grünbaum-Aksenov Theorem (extending Grötzsch’s Theorem) every planar graph with at most three triangles is 3-colorable. However, there are infinitely many planar 4-critical graphs with exactly four triangles. We describe all such graphs. This answers a question of Erdős from 1990.
AbstractGrötzsch proved that every planar triangle-free graph is 3-colorable. We prove that it has a...
A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up...
We describe an algorithm for generating all k-critical H-free graphs, based on a method of Hoang et ...
A recent lower bound on the number of edges in a k-critical n-vertex graph by Kostochka and Yancey y...
Aksenov proved that in a planar graph G with at most one triangle, every precoloring of a 4-cycle ca...
Aksenov proved that in a planar graph $G$ with at most one triangle, every precoloring of a 4-cycle ...
A graph G is uniquely k-colourable if the chromatic number of G is k and G has only one k-colouring ...
Non UBCUnreviewedAuthor affiliation: University of Illinois at Urbana-ChampaignFacult
AbstractThe conjecture of Dirac that every 4-critical planar graph has a vertex of degree at most 4 ...
AbstractFour problems of Grünbaum concerning 4-critical planar graphs with only vertices of valence ...
The famous four color theorem states that for all planar graphs, every vertex can be assigned one of...
In the first partial result toward Steinberg's now-disproved three coloring conjecture, Abbott and Z...
AbstractLet G be a 4-regular planar graph and suppose that G has a cycle decomposition S (i.e., each...
AbstractAksinov and Mel'nikov conjectured that every edge-critical non-3-colorable planar graph with...
AbstractIn 1970, Havel asked if each planar graph with the minimum distance, d∇, between triangles l...
AbstractGrötzsch proved that every planar triangle-free graph is 3-colorable. We prove that it has a...
A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up...
We describe an algorithm for generating all k-critical H-free graphs, based on a method of Hoang et ...
A recent lower bound on the number of edges in a k-critical n-vertex graph by Kostochka and Yancey y...
Aksenov proved that in a planar graph G with at most one triangle, every precoloring of a 4-cycle ca...
Aksenov proved that in a planar graph $G$ with at most one triangle, every precoloring of a 4-cycle ...
A graph G is uniquely k-colourable if the chromatic number of G is k and G has only one k-colouring ...
Non UBCUnreviewedAuthor affiliation: University of Illinois at Urbana-ChampaignFacult
AbstractThe conjecture of Dirac that every 4-critical planar graph has a vertex of degree at most 4 ...
AbstractFour problems of Grünbaum concerning 4-critical planar graphs with only vertices of valence ...
The famous four color theorem states that for all planar graphs, every vertex can be assigned one of...
In the first partial result toward Steinberg's now-disproved three coloring conjecture, Abbott and Z...
AbstractLet G be a 4-regular planar graph and suppose that G has a cycle decomposition S (i.e., each...
AbstractAksinov and Mel'nikov conjectured that every edge-critical non-3-colorable planar graph with...
AbstractIn 1970, Havel asked if each planar graph with the minimum distance, d∇, between triangles l...
AbstractGrötzsch proved that every planar triangle-free graph is 3-colorable. We prove that it has a...
A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up...
We describe an algorithm for generating all k-critical H-free graphs, based on a method of Hoang et ...