Displaying similar documents to “Observations on maps and δ-matroids”

On the simplex graph operator

Bohdan Zelinka (1998)

Discussiones Mathematicae Graph Theory

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A simplex of a graph G is a subgraph of G which is a complete graph. The simplex graph Simp(G) of G is the graph whose vertex set is the set of all simplices of G and in which two vertices are adjacent if and only if they have a non-empty intersection. The simplex graph operator is the operator which to every graph G assigns its simplex graph Simp(G). The paper studies graphs which are fixed in this operator and gives a partial answer to a problem suggested by E. Prisner.

Some news about oblique graphs

Andrey A. Dobrynin, Leonid S. Melnikov, Jens Schreyer, Hansjoachim Walther (2002)

Discussiones Mathematicae Graph Theory

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A k-gon α of a polyhedral graph G(V,E,F) is of type ⟨b₁,b₂,...,bₖ⟩ if the vertices incident with α in cyclic order have degrees b₁,b₂,...,bₖ and ⟨b₁,b₂,...,bₖ⟩ is the lexicographic minimum of all such sequences available for α. A polyhedral graph G is oblique if it has no two faces of the same type. Among others it is shown that an oblique graph contains vertices of degree 3.

Every 8-Traceable Oriented Graph Is Traceable

Susan A. van Aardt (2017)

Discussiones Mathematicae Graph Theory

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A digraph of order n is k-traceable if n ≥ k and each of its induced subdigraphs of order k is traceable. It is known that if 2 ≤ k ≤ 6, every k-traceable oriented graph is traceable but for k = 7 and for each k ≥ 9, there exist k-traceable oriented graphs that are nontraceable. We show that every 8-traceable oriented graph is traceable.