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3coloring trianglefree planar graphs with a precolored 8cycle
, 2013
"... Let G be a planar trianglefree graph and led C be a cycle in G of length at most 8. We characterize all situations where a 3coloring of C does not extend to a proper 3coloring of the whole graph. ..."
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Cited by 3 (2 self)
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Let G be a planar trianglefree graph and led C be a cycle in G of length at most 8. We characterize all situations where a 3coloring of C does not extend to a proper 3coloring of the whole graph.
Fast 3Coloring TriangleFree Planar Graphs
 12th Annual European Symposium (ESA’04), Lecture Notes In Computer Science, (c
, 2004
"... Abstract. We show the first o(n 2) algorithm for coloring vertices of trianglefree planar graphs using three colors. The time complexity of the algorithm is O(nlog n). Our approach can be also used to designO(npolylog n)time algorithms for two other similar coloring problems. A remarkable ingredien ..."
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Cited by 14 (1 self)
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Abstract. We show the first o(n 2) algorithm for coloring vertices of trianglefree planar graphs using three colors. The time complexity of the algorithm is O(nlog n). Our approach can be also used to designO(npolylog n)time algorithms for two other similar coloring problems. A remarkable
Median Graphs and TriangleFree Graphs
, 1997
"... Let M(m;n) be the complexity of checking whether a graph G with m ..."
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Cited by 31 (14 self)
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Let M(m;n) be the complexity of checking whether a graph G with m
Coloring trianglefree graphs on surfaces (Extended Abstract)
"... Gimbel and Thomassen asked whether 3colorability of a trianglefree graph drawn on a fixed surface can be tested in polynomial time. We settle the question by giving a lineartime algorithm for every surface which combined with previous results gives a lineartime algorithm to compute the chromatic ..."
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Gimbel and Thomassen asked whether 3colorability of a trianglefree graph drawn on a fixed surface can be tested in polynomial time. We settle the question by giving a lineartime algorithm for every surface which combined with previous results gives a lineartime algorithm to compute the chromatic
Coloring of trianglefree graphs on the double torus
"... trianglefree graphs on the double torus ..."
Independent Sets In TriangleFree Cubic Planar Graphs
"... We prove that every trianglefree planar graph on n vertices with maximum degree three has an independent set with size at least 3/8 n. This was suggested and later conjectured by Albertson, Bollobás, and Tucker. ..."
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Cited by 13 (1 self)
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We prove that every trianglefree planar graph on n vertices with maximum degree three has an independent set with size at least 3/8 n. This was suggested and later conjectured by Albertson, Bollobás, and Tucker.
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Fine structure of 4critical trianglefree graphs III. General surfaces
, 2015
"... Dvořák, Král’ and Thomas [4, 6] gave a description of the structure of trianglefree graphs on surfaces with respect to 3coloring. Their description however contains two substructures (both related to graphs embedded in plane with two precolored cycles) whose coloring properties are not entirel ..."
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Dvořák, Král’ and Thomas [4, 6] gave a description of the structure of trianglefree graphs on surfaces with respect to 3coloring. Their description however contains two substructures (both related to graphs embedded in plane with two precolored cycles) whose coloring properties
SUBEXPONENTIALLY MANY 3COLORINGS OF TRIANGLEFREE PLANAR GRAPHS
, 2010
"... Thomassen conjectured that every trianglefree planar graph on n vertices has exponentially many 3colorings, and proved that it has at least 2n1/12 /20000 √ distinct 3colorings. We show n/362 that it has at least 2 distinct 3colorings. ..."
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Thomassen conjectured that every trianglefree planar graph on n vertices has exponentially many 3colorings, and proved that it has at least 2n1/12 /20000 √ distinct 3colorings. We show n/362 that it has at least 2 distinct 3colorings.
Results 1  10
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49,227