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Title: | The saturation number for the length of degree monotone paths |
Authors: | Caro, Yair Lauri, Josef Zarb, Christina |
Keywords: | Graph theory Paths and cycles (Graph theory) Mathematics -- Charts, diagrams, etc. |
Issue Date: | 2015 |
Publisher: | Uniwersytet Zielonogorski * Wydzial Matematyki, Informatyli i Ekonometrii,Technical University Zielona Gora, Institute of Mathematics |
Citation: | Caro, Y., Lauri, J., & Zarb, C. (2015). The saturation number for the length of degree monotone paths. Discussiones Mathematicae Graph Theory, 35, 557-569. |
Abstract: | A degree monotone path in a graph G is a path P such that the sequence of degrees of the vertices in the order in which they appear on P is monotonic. The length (number of vertices) of the longest degree monotone path in G is denoted by mp(G). This parameter, inspired by the well-known Erd˝osSzekeres theorem, has been studied by the authors in two earlier papers. Here we consider a saturation problem for the parameter mp(G). We call G saturated if, for every edge e added to G, mp(G + e) > mp(G), and we define h(n, k) to be the least possible number of edges in a saturated graph G on n vertices with mp(G) < k, while mp(G+e) ≥ k for every new edge e. We obtain linear lower and upper bounds for h(n, k), we determine exactly the values of h(n, k) for k = 3 and 4, and we present constructions of saturated graphs. |
URI: | https://www.um.edu.mt/library/oar/handle/123456789/112480 |
Appears in Collections: | Scholarly Works - FacSciMat |
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The_saturation_number_for_the_length_of_degree_monotone_paths_2015.pdf Restricted Access | 150.05 kB | Adobe PDF | View/Open Request a copy |
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