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This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. The limit theorems are universal depending solely on the limiting behavior ...
Acyclic edge-coloring using entropy compression     Acyclic edge-coloring  entropy compression  Combinatorics       font style='font-size:12px;'> 2012/6/29
An edge-coloring of a graph G is acyclic if it is a proper edge-coloring of G and every cycle contains at least three colors. We prove that every graph with maximum degree Delta has an acyclic edge-co...
Coloring claw-free graphs with Δ-1 colors     Coloring claw-free graphs  Combinatorics       font style='font-size:12px;'> 2012/6/25
We prove that every claw-free graph $G$ that doesn't contain a clique on $\Delta(G) \geq 9$ vertices can be $\Delta(G) - 1$ colored.
Coloring, location and domination of corona graphs     Coloring  domination  location  Roman domination  corona graphs       font style='font-size:12px;'> 2012/4/18
A vertex coloring of a graph $G$ is an assignment of colors to the vertices of $G$ such that every two adjacent vertices of $G$ have different colors. A coloring related property of a graphs is also a...
Acyclic edge coloring of sparse graphs     acyclic  coloring  average degree  critical       font style='font-size:12px;'> 2012/2/29
A proper edge coloring of a graph $G$ is called acyclic if there is no bichromatic cycle in $G$. The acyclic chromatic index of $G$, denoted by $\chi'_a(G)$, is the least number of colors $k$ such tha...
Abstract: We give a simpler proof of Seymour's Theorem on edge-coloring series-parallel multigraphs and derive a linear-time algorithm to check whether a given series-parallel multigraph can be colore...
Abstract: For many random constraint satisfaction problems such as random satisfiability or random graph or hypergraph coloring, the best current estimates of the threshold for the existence of soluti...
Abstract: Conflict-free coloring is a kind of coloring of hypergraphs requiring each hyperedge to have a color which appears only once. More generally, there are $k$-conflict-free coloring ($k$-CF-col...
Edge Coloring of Triangle-Free 1-Planar Graphs      Edge Coloring  Triangle-Free 1-Planar Graphs        font style='font-size:12px;'> 2011/3/1
Edge Coloring of Triangle-Free 1-Planar Graphs.
Vertex, edge and total coloring in spider graphs     Vertex coloring  Edge- coloring  Total coloring       font style='font-size:12px;'> 2010/9/13
In this paper we investigate the vertex chromatic number, the edge chromatic number, and the total chromatic number in Spider graphs.
List VEF coloring of planar graphs     Planar Graphs  list coloring  VEF coloring       font style='font-size:12px;'> 2010/9/14
In this paper the new coloring of planar, VEF-coloring, will be introduced. A VEF coloring of a simple planar graph G is a proper coloring of all elements, including vertices, edges and faces of G. We...

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