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arXiv · 1812.09422

Packing functions and graphs with perfect closed neighbourhood matrices

Mariana Escalante·Erica Hinrichsen·Valeria. Leoni
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Abstract

In this work we consider a straightforward linear programming formulation of the recently introduced $\{k\}$-packing function problem in graphs, for each fixed value of the positive integer number $k$. We analyse a special relation between the case $ k = 1$ and $ k \geq 2$ and give a sufficient condition for optimality ---the perfection--- of the closed neighbourhood matrix $N[G]$ of the input graph $G$. We begin a structural study of graphs satisfying this condition. In particular, we look for a characterization of graphs that have perfect closed neighbourhood matrices which involves the property of being a clique-node matrix of a perfect graph. We present a necessary and sufficient condition for a graph to have a clique-node closed neighbourhood matrix. Finally, we study the perfection of the graph of maximal cliques associated to $N[G]$.

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Mariana Escalante, Erica Hinrichsen, Valeria. Leoni. 2018-12-22. Packing functions and graphs with perfect closed neighbourhood matrices. https://arxiv.org/abs/1812.09422

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