@article {sousa:7-cycle, title = {Decompositions of graphs into cycles of length seven and single edges}, journal = {Ars Combinatoria}, volume = {119}, year = {2015}, pages = {321-329}, abstract = {

Given graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let f_H(n) be the smallest number t such that any graph G of order n admits an H-decomposition with at most t parts. Here we study the case when H=C_7, that is, the cycle of length 7 and prove that f_{C_7}(n)=\lfloor n^2/4 \rfloor for all n>=10.

}, attachments = {https://docentes.fct.unl.pt/sites/default/files/tmjs/files/20xx-7-cycle.pdf}, author = {Sousa, Teresa} } @article {sousa:clique-extension, title = {Decompositions of graphs into a given clique-extension}, journal = {Ars Combinatoria}, volume = {100}, number = {1}, year = {2011}, pages = {465{\textendash}472}, abstract = {

For r>=3, a clique-extension of order r+1 is a connected graph that consists of a Kr plus another vertex adjacent to at most r-1 vertices of Kr. In this paper we consider the problem of finding the smallest number t such that any graph G of order n admits a decomposition into edge disjoint copies of a fixed graph H and single edges with at most t elements. Here we solve the case when H is a fixed clique-extension of order r+1, for all r>=3 and will also obtain all extremal graphs. This work extends results proved by Bollob{\'a}s [Math.\ Proc.\ Cambridge Philosophical Soc 79 (1976) 19--24] for cliques.

}, url = {http://www.combinatorialmath.ca/arscombinatoria/vol100.html}, attachments = {https://docentes.fct.unl.pt/sites/default/files/tmjs/files/2011-04-clique_extension.pdf}, author = {Sousa, Teresa} } @article {sousa:5-cycle, title = {Decompositions of graphs into 5-cycles and other small graphs}, journal = {Electronic Journal of Combinatorics}, volume = {12}, year = {2005}, pages = {R49, 7 pp.}, abstract = {

If H is a family of graphs, then an H-decomposition of a graph G is a partition of the edges of G each element of which induces a copy of a graph in G.
This paper addresses the problem of finding the number φ(n,H), the smallest number k such that every graph on n vertices has an H-decomposition with at most k elements. φ(n,H) is found in the cases when H={K2,C5}; when H={K2,C5+e}, where e is a chord of the C5; when H={K2,K4-e}; and when H={K2,K3+e}, where e is a pendant edge added to one vertex in the K3.

}, issn = {1077-8926}, url = {http://www.combinatorics.org/Volume_12/PDF/v12i1r49.pdf}, attachments = {https://docentes.fct.unl.pt/sites/default/files/tmjs/files/2005-09-5-cycle.pdf}, author = {Sousa, Teresa} }