Resumen en Inglés:

This is an account of Jayme's contributions to Graph Theory and Computer Science. Due to restrictions in length, it is not possible to provide an in-depth coverage of every aspect of Jayme's extensive scientific activities. Thus, I describe in detail only some of his principal contributions, touch upon some and merely list the other articles. I found it easier to write the article in the first person, as though it is an account of a previously given lecture.

Resumen en Inglés:

This paper considers a problem of coupled task scheduling on one processor, where all processing times are equal to 1, the gap has exact length h, precedence constraints are strict and the criterion is to minimise the schedule length. This problem is introduced e.g. in systems controlling radar operations. We show that the general problem is NP-hard.

Resumen en Inglés:

As usual, for graphs <FONT FACE=Symbol>G</font>, G, and H, we write <FONT FACE=Symbol>G ®</FONT> (G, H) to mean that any red-blue colouring of the edges of gamma contains a red copy of G or a blue copy of H. A pair of graphs (G, H) is said to be Ramsey-infinite if there are infinitely many minimal graphs F for which we have <FONT FACE=Symbol>G ®</FONT> (G, H). Let l > 4 be an integer. We show that if H is a 2-connected graph that does not contain induced cycles of length at least l, then the pair (Ck,H) is Ramsey-infinite for any k > l, where Ck denotes the cycle of length k.

Resumen en Inglés:

This paper deals with edge-clique graphs and with the lambda-coloring problem when restricted to this class. A characterization of edge-clique graphs of out-erplanar graphs is given; a complete description of edge-clique graphs of threshold graphs is presented and a linear time algorithm for lambda-coloring the edge-clique graph of a threshold graph is provided. A survey on the lambda-coloring problem, when restricted to edge-clique graphs, is reported.

Resumen en Inglés:

The Helly defect of a graph G is the smallest integer i such that the iterated clique graph Ki(G) is clique-Kelly. We prove that it is NP-hard to decide whether the Helly defect of G is at most 1.

Resumen en Inglés:

In this text we attempt to unify many results about the K operator based on a new theory involving graphs, families and operators. We are able to build an ''operator algebra'' that helps to unify and automate arguments. In addition, we relate well-known properties, such as the Helly property, to the families and the operators. As a result, we deduce many classic results in clique graph theory from the basic fact that CS = I for conformal, reduced families. This includes Hamelink's construction, Roberts and Spencer theorem, and Ban-delt and Prisner's partial characterization of clique-fixed classes [2]. Furthermore, we show the power of our approach proving general results that lead to polynomial recognition of certain graph classes.

Resumen en Inglés:

We consider producing permutations and combinations in lexicographical order. Except for the array that holds the combinatorial object, we require only O(1) extra storage. The production of the next item requires O(1) amortized time.

Resumen en Inglés:

If G is a graph, its clique graph K(G) is the intersection graph of all its (maximal) cliques. The complex G<FONT FACE=Symbol></FONT> of a graph G is the simplicial complex whose simplexes are the vertex sets of the complete subgraphs of G. Here we study a sufficient condition for G<FONT FACE=Symbol></FONT> and K(G)<FONT FACE=Symbol></FONT> to be homotopic. Applying this result to Whitney triangulations of surfaces, we construct an infinite family of examples which solve in the affirmative Prisner's open problem 1 in Graph Dynamics (Longman, Harlow, 1995): Are there finite connected graphs G that are periodic under K and where the second modulo 2 Betti number is greater than 0?