The circular chromatic number of a graph is a well-studied refinement of the chromatic number. Circular-perfect graphs form a superclass of perfect graphs defined by means of this more general coloring concept. This paper studies claw-free circular-perfect graphs. First we prove that ifG is a connected claw-free circular-perfect graph with χ(G) > ω(G), then min{α(G), ω(G)} = 2. We use this resu...

The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit design, synchronous systems, computer systems, and very-large-scale integration (VLSI) circuits. The FVS problem is known to be NP-hard for simple graphs, but polynomial-time algorithm...

A circular-arc graph is the intersection graph of arcs of a circle. A Helly circular-arc graph is a circular-arc graph admitting a model whose arcs satisfy the Helly property. A clique-independent set of a graph is a set of pairwise disjoint cliques of the graph. It is NP-hard to compute the maximum cardinality of a clique-independent set for a general graph. In the present paper, we propose al...

For 1 ≤ d ≤ k, let Kk/d be the graph with vertices 0, 1, · · · , k − 1, in which i ∼ j if d ≤ |i − j| ≤ k − d. The circular chromatic number χc(G) of a graph G is the minimum of those k/d for which G admits a homomorphism to Kk/d. The circular clique number ωc(G) of G is the maximum of those k/d for which Kk/d admits a homomorphism to G. A graph G is circular perfect if for every induced subgra...

The Hadwiger number of a graph G is the largest integer n for which the complete graph on n vertices is a minor of G. Hadwiger conjectured that for any graph G, ,where is the chromatic number of G. We will address Hadwiger’s conjecture for circular arc graphs and their subfamilies. Circular arc graphs are graphs whose vertices can be represented as arcs on a circle such that any two vertices ar...

A radiation pattern synthesis technique for large planar arrays with active element pattern (AEP) method and fine-grained parallel micro-genetic algorithm (FGPMGA) is presented. Based on the AEP method, the mutual coupling between array elements can be taken into account. Analysis problems of large rectangular and triangular grid planar arrays are divided into small linear array problems. And f...