Abstract
Graphs of separability at most k are defined as graphs in which every two non-adjacent vertices are separated by a set of at most k other vertices. For k ∈ {0,1}, the only connected graphs of separability at most k are complete graphs and block graphs, respectively. For k ≥ 3, graphs of separability at most k form a rich class of graphs containing all graphs of maximum degree k. Graphs of separability at most 2 generalize complete graphs, cycles and trees. We prove several characterizations of graphs of separability at most 2 and examine some of their consequences.
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Cicalese, F., Milanič, M. (2011). Graphs of Separability at Most Two: Structural Characterizations and Their Consequences. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2010. Lecture Notes in Computer Science, vol 6460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19222-7_30
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DOI: https://doi.org/10.1007/978-3-642-19222-7_30
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