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The twocoloring . . . colorings of planar graphs
, 2009
"... The twocoloring number of graphs, which was originally introduced in the study of the game chromatic number, also gives an upper bound on the degenerate chromatic number as introduced by Borodin. It is proved that the twocoloring number of any planar graph is at most nine. As a consequence, the de ..."
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The twocoloring number of graphs, which was originally introduced in the study of the game chromatic number, also gives an upper bound on the degenerate chromatic number as introduced by Borodin. It is proved that the twocoloring number of any planar graph is at most nine. As a consequence
On the Queue Number of Planar Graphs
, 2010
"... We prove that planar graphs have O(log 4 n) queue number, thus improving upon the previous O ( √ n) upper bound. Consequently, planar graphs admit 3D straightline crossingfree grid drawings in O(n log c n) volume, for some constant c, thus improving upon the previous O(n 3/2) upper bound. 2 1 ..."
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Cited by 8 (0 self)
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We prove that planar graphs have O(log 4 n) queue number, thus improving upon the previous O ( √ n) upper bound. Consequently, planar graphs admit 3D straightline crossingfree grid drawings in O(n log c n) volume, for some constant c, thus improving upon the previous O(n 3/2) upper bound. 2 1
DEGENERATE AND STAR COLORINGS OF GRAPHS ON SURFACES
, 2009
"... We study the degenerate, the star and the degenerate star chromatic numbers and their relation to the genus of graphs. As a tool we prove the following strengthening of a result of Fertin et al. [8]: If G is a graph of maximum degree Δ, then G admits a degenerate star coloring using O(Δ 3/2) colors. ..."
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We study the degenerate, the star and the degenerate star chromatic numbers and their relation to the genus of graphs. As a tool we prove the following strengthening of a result of Fertin et al. [8]: If G is a graph of maximum degree Δ, then G admits a degenerate star coloring using O(Δ 3/2) colors
Thresholds for Path Colorings of Planar Graphs
, 2005
"... A graph is path kcolorable if it has a vertex kcoloring in which the subgraph induced by each color class is a disjoint union of paths. A graph is path kchoosable if, whenever each vertex is assigned a list of k colors, such a coloring exists in which each vertex receives a color from its list. I ..."
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. It is known that every planar graph is path 3colorable [15, 13] and, in fact, path 3choosable [14]. We investigate which planar graphs are path 2colorable or path 2choosable. We seek results of a “threshold ” nature: on one side of a threshold, every graph is path 2choosable, and there is a fast coloring
ON THE COLORABILITY OF GRAPHS DECOMPOSABLE INTO DEGENERATE GRAPHS WITH SPECIFIED DEGENERACY
"... every subgraph of which has minimal at most m. An (mI, m2,..., the set of which can be partitioned into s sets generating rpc,,,prtlvplv We conjecture that such a graph is)J colorable. Partial results is settled. ~VU<A>"Uv',"". but not even Tarsi's case: ml = 1, m2 = 2 ..."
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every subgraph of which has minimal at most m. An (mI, m2,..., the set of which can be partitioned into s sets generating rpc,,,prtlvplv We conjecture that such a graph is)J colorable. Partial results is settled. ~VU<A>"Uv',"". but not even Tarsi's case: ml = 1, m2
Acyclic List 7Coloring Of Planar Graphs
 KOSTOCHKA, ANDRÉ RASPAUD, AND ÉRIC SOPENA. Acyclic
, 2001
"... . The acyclic list chromatic number of every 1planar graph is proved to be at most 7 and is conjectured to be at most 5. Keywords. Acyclic coloring, List coloring, Acyclic list coloring. 1 ..."
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Cited by 11 (1 self)
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. The acyclic list chromatic number of every 1planar graph is proved to be at most 7 and is conjectured to be at most 5. Keywords. Acyclic coloring, List coloring, Acyclic list coloring. 1
Algorithms for the Total Colorings of Graphs
, 2002
"... This thesis presents efficient algorithms for finding total colorings of graphs. A total coloring of a graph G is a coloring of all vertices and edges of G such that any two adjacent vertices receive different colors, any two adjacent edges receive different colors, and any edge receives a color dif ..."
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different from the colors of its two ends. The total coloring problem asks to find a total coloring of a given graph with the minimum number of colors. This problem is NPhard and hence it is very unlikely that there is an efficient algorithm to solve the total coloring problem. On the other hand
Results 1  10
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29,508