A d-graph G = (V ; E1, . . . , Ed) is a complete graph whose edges are arbitrarily partitioned into d subsets (colored with d colors); G is a Gallai d-graph if it contains no three-colored triangle ∆; furthermore, G is a CIS d-graph if ⋂d i=1 Si 6= ∅ for every set-family S = {Si | i ∈ [d]}, where Si ⊆ V is a maximal independent set of Gi = (V,Ei), the ith chromatic component of G, for all i ∈ [...

A general partition graph (gpg) is an intersection graph G on a set S so that for every maximal independent set M of vertices in G, the subsets assigned to the vertices in M partition S. These graphs have been characterized by the presence of special clique covers. The Triangle Condition T for a graph G is that for any maximal independent set M and any edge uv in G M, there is a vcrtex W E M so...

We study different classes of digraphs, which are generalizations of tournaments, to have the property of possessing a maximal independent set intersecting every non-augmentable path (in particular, every longest path). The classes are the arclocal tournament, quasi-transitive, locally in-semicomplete (out-semicomplete), and semicomplete k-partite digraphs. We present results on strongly intern...

The square G2 of a graph G is defined on the vertex set of G in such a way that distinct vertices with distance at most two in G are joined by an edge. We study the chromatic number of the square of the Cartesian product Cm2Cn of two cycles and show that the value of this parameter is at most 7 except when m = n = 3, in which case the value is 9, and when m = n = 4 or m = 3 and n = 5, in which ...

A theorem of O’Nan and Scott [6]; [2, Chapter 4] restricts the possibilities for maximal subgroups of finite symmetric groups: they are of six types of which the first four are explicitly known, the fifth involves a finite simple group, and the sixth an action of a simple group. This result, in conjunction with the Classification of Finite Simple Groups, has a number of consequences. In particu...

Existing work that schedules concurrent transmissions collision-free suffers from low channel utilization. We propose the Optimal Node Activation Multiple Access (ONAMA) protocol to achieve maximal channel spatial reuse through a distributed maximal independent set (DMIS) algorithm. To overcome DMIS’s excessive delay in finding a maximal independent set, we devise a novel technique called pipel...

In this paper we study the question of existence of a cycle basis (that is, a basis consisting only of cycles) for the lattice Z(M) generated by the cycles of a binary matroid M. We show that, if M has no Fano dual minor, then the set of fundamental circuits of any maximal independent set of M can be completed to a cycle basis of Z(M); moreover, for any one-element extension M 0 of such matroid...

Given a graph G = (V,E), the Maximum Independent Set problem (MIS) aims to determine a subset S ⊆ V of maximum cardinality such that no two vertices of S are adjacent. This paper presents a general Swap-Based Tabu Search (SBTS) for solving the MIS. SBTS integrates distinguished features including a general and unified (k, 1)-swap operator, four constrained neighborhoods and specific rules for n...

Cycle bases for lattices of binary matroids with no Fano dual minor and their one-element extensions Abstract In this paper we study the question of existence of a cycle basis (that is, a basis consisting only of cycles) for the lattice Z(M) generated by the cycles of a binary matroid M. We show that, if M has no Fano dual minor, then the set of fundamental circuits of any maximal independent s...

A graph G is well-covered if every maximal independent set has the same cardinality. Let sk denote the number of independent sets of cardinality k, and define the independence polynomial of G to be S(G, z) = ∑ skz k. This paper develops a new graph theoretic operation called power magnification that preserves well-coveredness and has the effect of multiplying an independence polynomial by zc wh...