Displaying similar documents to “On Path-Pairability in the Cartesian Product of Graphs”

A Note on Path Domination

Liliana Alcón (2016)

Discussiones Mathematicae Graph Theory

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We study domination between different types of walks connecting two non-adjacent vertices u and v of a graph (shortest paths, induced paths, paths, tolled walks). We succeeded in characterizing those graphs in which every uv-walk of one particular kind dominates every uv-walk of other specific kind. We thereby obtained new characterizations of standard graph classes like chordal, interval and superfragile graphs.

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...

Path-Neighborhood Graphs

R.C. Laskar, Henry Martyn Mulder (2013)

Discussiones Mathematicae Graph Theory

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A path-neighborhood graph is a connected graph in which every neighborhood induces a path. In the main results the 3-sun-free path-neighborhood graphs are characterized. The 3-sun is obtained from a 6-cycle by adding three chords between the three pairs of vertices at distance 2. A Pk-graph is a path-neighborhood graph in which every neighborhood is a Pk, where Pk is the path on k vertices. The Pk-graphs are characterized for k ≤ 4.

3-Paths in Graphs with Bounded Average Degree

Stanislav Jendrol′, Mária Maceková, Mickaël Montassier, Roman Soták (2016)

Discussiones Mathematicae Graph Theory

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In this paper we study the existence of unavoidable paths on three vertices in sparse graphs. A path uvw on three vertices u, v, and w is of type (i, j, k) if the degree of u (respectively v, w) is at most i (respectively j, k). We prove that every graph with minimum degree at least 2 and average degree strictly less than m contains a path of one of the types [...] Moreover, no parameter of this description can be improved.