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UNIVERSAL POISSON AND NORMAL LIMIT THEOREMS IN GRAPH COLORING PROBLEMS WITH CONNECTIONS TO EXTREMAL COMBINATORICS
Limit theorem the monochromatic edge evenly random colors random graph
2015/7/7
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
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...
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
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...
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...
Edge-coloring series-parallel multigraphs
Edge-coloring series-parallel multigraphs Data Structures and Algorithms Combinatorics
2011/10/9
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...
The condensation transition in random hypergraph 2-coloring
random structures phase transitions hypergraph 2-coloring second moment method
2011/9/5
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...
$k$-Conflict-Free Coloring and $k$-Strong-Conflict-Free Coloring for One Class of Hypergraphs and Online $k$-Conflict-Free Coloring
Hypergraphs Online $k$-Conflict-Free Coloring Combinatorics
2011/8/22
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.
Vertex, edge and total coloring in spider graphs
Vertex coloring Edge- coloring Total coloring
2010/9/13
In this paper we investigate the vertex chromatic number, the edge chromatic number, and the total chromatic number in Spider graphs.
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...