Displaying similar documents to “The neighborhood characteristic parameter for graphs.”

A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs

Wojciech Wide (2017)

Discussiones Mathematicae Graph Theory

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A graph G on n vertices is said to be pancyclic if it contains cycles of all lengths k for k ∈ {3, . . . , n}. A vertex v ∈ V (G) is called super-heavy if the number of its neighbours in G is at least (n+1)/2. For a given graph H we say that G is H-f1-heavy if for every induced subgraph K of G isomorphic to H and every two vertices u, v ∈ V (K), dK(u, v) = 2 implies that at least one of them is super-heavy. For a family of graphs H we say that G is H-f1-heavy, if G is H-f1-heavy for...

Fruit salad.

Gyárfás, András (1997)

The Electronic Journal of Combinatorics [electronic only]

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Star-Cycle Factors of Graphs

Yoshimi Egawa, Mikio Kano, Zheng Yan (2014)

Discussiones Mathematicae Graph Theory

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A spanning subgraph F of a graph G is called a star-cycle factor of G if each component of F is a star or cycle. Let G be a graph and f : V (G) → {1, 2, 3, . . .} be a function. Let W = {v ∈ V (G) : f(v) = 1}. Under this notation, it was proved by Berge and Las Vergnas that G has a star-cycle factor F with the property that (i) if a component D of F is a star with center v, then degF (v) ≤ f(v), and (ii) if a component D of F is a cycle, then V (D) ⊆ W if and only if iso(G − S) ≤ Σx∈S...

Maxclique and Unit Disk Characterizations of Strongly Chordal Graphs

Pablo De Caria, Terry A. McKee (2014)

Discussiones Mathematicae Graph Theory

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Maxcliques (maximal complete subgraphs) and unit disks (closed neighborhoods of vertices) sometime play almost interchangeable roles in graph theory. For instance, interchanging them makes two existing characterizations of chordal graphs into two new characterizations. More intriguingly, these characterizations of chordal graphs can be naturally strengthened to new characterizations of strongly chordal graphs