Displaying similar documents to “ H -decompositions of r -graphs when H is an r -graph with exactly 2 edges.”

Decompositions of multigraphs into parts with two edges

Jaroslav Ivančo, Mariusz Meszka, Zdzisław Skupień (2002)

Discussiones Mathematicae Graph Theory

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Given a family 𝓕 of multigraphs without isolated vertices, a multigraph M is called 𝓕-decomposable if M is an edge disjoint union of multigraphs each of which is isomorphic to a member of 𝓕. We present necessary and sufficient conditions for the existence of such decompositions if 𝓕 comprises two multigraphs from the set consisting of a 2-cycle, a 2-matching and a path with two edges.

On edge detour graphs

A.P. Santhakumaran, S. Athisayanathan (2010)

Discussiones Mathematicae Graph Theory

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For two vertices u and v in a graph G = (V,E), the detour distance D(u,v) is the length of a longest u-v path in G. A u-v path of length D(u,v) is called a u-v detour. A set S ⊆V is called an edge detour set if every edge in G lies on a detour joining a pair of vertices of S. The edge detour number dn₁(G) of G is the minimum order of its edge detour sets and any edge detour set of order dn₁(G) is an edge detour basis of G. A connected graph G is called an edge detour graph if it has...