We study online interval coloring problems with bandwidth. We are interested in some variants motivated by bin packing problems. Specifically we consider open-end coloring, cardinality constrained coloring, coloring with vector constraints and finally a combination of both the cardinality and the vector constraints. We construct competitive algorithms for each of the variants. Additionally, we ...

Let G be a simple graph on n vertices, and let χG(λ) denote the chromatic polynomial of G. In this paper, we define the cyclic coloring complex, ∆(G), and determine the dimensions of its homology groups for simple graphs. In particular, we show that if G has r connected components, the dimension of (n− 3)rd homology group of ∆(G) is equal to (n− (r+ 1)) plus 1 r! |χG(0)|, where χG is the rth de...

Abstract Oriented coloring of an oriented graph G is arc-preserving homomorphism from into a tournament H . We say that the universal for family graphs $$\mathcal {C}$$ C if every $$G\in \mathcal G ∈ there exists are interested in finding orientations c...

We investigate the rare baryonic exclusive decays of Λb → Λll (l = e, μ, τ) with polarized Λ. Under the approximation of the heavy quark effective theory (HQET), in the standard model we derive the differential decay rates and various polarization asymmetries by including lepton mass effects. We find that with the long-distance effects the decay branching ratios are 5.3× 10 for Λb → Λll (l = e,...

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 will give two conjectures for the upper bound of VEF and VEF-list coloring of a simple planar graph. However, we will prove these conjectures for planar graphs with a maximum degree of at least 12...

An ℓ-facial edge-coloring of a plane graph is coloring its edges such that any two at distance most ℓ on boundary walk face receive distinct colors. It the variant vertex coloring, which arose as generalization well-known cyclic coloring. conjectured 3ℓ+1 colors suffice for an graph. The conjecture has only been confirmed ℓ≤2, and in this paper, we prove validity ℓ=3.