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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 ...
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.
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...
In multi-hop radio networks, such as wireless ad-hoc and sensor networks, nodes employ a MAC (Medium Access Control) protocol such as TDMA to coordinate accesses to the shared medium and to avoid inte...
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...
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...
An experiment was conducted to evaluate the effect of different levels of extracted pigment from Dietzia natronolimnaea biomass as a source of canthaxanthin in comparison with synthetic canthaxanthin ...

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