In the past 30 years, results regarding special classes of integer linear (and, more generally, convex) programs flourished. Applications in the field of parameterized complexity were called for and the call has been answered, demonstrating the importance of connecting the two fields. The classical result due to Lenstra states that solving Integer Linear Programming in fixed dimension is polyno...

an acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. the acyclic chromatic index of a graph $g$ denoted by $chi_a '(g)$ is the minimum number $k$ such that there is an acyclic edge coloring using $k$ colors. the maximum degree in $g$ denoted by $delta(g)$, is the lower bound for $chi_a '(g)$. $p$-cuts introduced in this paper acts as a powerfu...

Defective coloring is a variant of the traditional vertex-coloring in which adjacent vertices are allowed to have the same color, as long as the induced monochromatic components have a certain structure. Due to its important applications, as for example in the bipartisation of graphs, this type of coloring has been extensively studied, mainly with respect to the size, degree, diameter, and acyc...

In FOCS 2002, Even et al. showed that any set of n discs in the plane can be Conflict-Free colored with a total of at most O(log n) colors. That is, it can be colored with O(log n) colors such that for any (covered) point p there is some disc whose color is distinct from all other colors of discs containing p. They also showed that this bound is asymptotically tight. In this paper we prove the ...

It is well known that the vertices of a planar graph can be colored with no more than four colors [l]. However, the rather detailed proof of this fact leads to a @(n*) algorithm for determining such a coloring. To yield faster algorithms, several authors have considered generating a fivecoloring rather than a four-coloring [4]. Recently, two different approaches to five-coloring planar graphs h...

Linear Linkage Encoding (LLE) is a recently proposed representation scheme for evolutionary algorithms. This representation has been used only in data clustering. However, it is also suitable for grouping problems. In this paper, we investigate LLE on two grouping problems; graph coloring and exam timetabling. Two crossover operators suitable for LLE are proposed and compared to the existing on...

Linear scan register allocation is a fast global register allocation first presented in [PS99] as an alternative to the more widely used graph coloring approach. In this paper, I apply the linear scan register allocation algorithm in a system with SSA form and show how to improve the algorithm by taking advantage of lifetime holes and memory operands, and also eliminate the need for reserving r...

The radio k-chromatic number $$rc_k(G)$$ of a graph G is the minimum integer $$\lambda $$ such that there exists function $$\phi : V(G) \rightarrow \{0,1,\cdots , \lambda \}$$ satisfying $$|\phi (u)-\phi (v)| \ge k+1 - d(u,v)$$ where d(u, v) denotes distance between u and v. To date, several upper lower bounds $$rc_k(\cdot )$$ established for different families. One most notable works in this d...