Displaying similar documents to “On systems of graphs intersecting in paths”

On Path-Pairability in the Cartesian Product of Graphs

Gábor Mészáros (2016)

Discussiones Mathematicae Graph Theory

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We study the inheritance of path-pairability in the Cartesian product of graphs and prove additive and multiplicative inheritance patterns of path-pairability, depending on the number of vertices in the Cartesian product. We present path-pairable graph families that improve the known upper bound on the minimal maximum degree of a path-pairable graph. Further results and open questions about path-pairability are also presented.

Asteroidal Quadruples in non Rooted Path Graphs

Marisa Gutierrez, Benjamin Lévêque, Silvia B. Tondato (2015)

Discussiones Mathematicae Graph Theory

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A directed path graph is the intersection graph of a family of directed subpaths of a directed tree. A rooted path graph is the intersection graph of a family of directed subpaths of a rooted tree. Rooted path graphs are directed path graphs. Several characterizations are known for directed path graphs: one by forbidden induced subgraphs and one by forbidden asteroids. It is an open problem to find such characterizations for rooted path graphs. For this purpose, we are studying in this...

Superstable graphs

Heinrich Herre, Allan Mekler, Kenneth Smith (1983)

Fundamenta Mathematicae

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