منابع مشابه
Immersion in four-edge-connected graphs
Fix g > 1. Every graph of large enough tree-width contains a g × g grid as a minor; but here we prove that every four-edge-connected graph of large enough tree-width contains a g × g grid as an immersion (and hence contains any fixed graph with maximum degree at most four as an immersion). This result has a number of applications.
متن کاملGenerating connected and 2-edge connected graphs
We focus on the algorithm underlying the main result of [6]. This is an algebraic formula to generate all connected graphs in a recursive and efficient manner. The key feature is that each graph carries a scalar factor given by the inverse of the order of its group of automorphisms. In the present paper, we revise that algorithm on the level of graphs. Moreover, we extend the result subsequentl...
متن کاملSufficient conditions for maximally edge-connected and super-edge-connected
Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...
متن کاملmaximally edge - connected and super - edge - connected graphs ∗
Let G be a connected graph with minimum degree δ and edgeconnectivity λ. A graph is maximally edge-connected if λ = δ, and it is superedge-connected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. In this paper, we show that a connected graph or a connected triangle-free graph is maximally edge-connected or sup...
متن کاملGenerating Internally Four-Connected Graphs
A graph is a minor of another if the first can be obtained from a subgraph of the second by contracting edges. A graph G is internally 4-connected if it is simple, 3-connected, has at least five vertices, and if for every partition (A, B) of the edge-set of G, either |A| ≤ 3, or |B| ≤ 3, or at least four vertices of G are incident with an edge in A and an edge in B. We prove that if H and G are...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2016
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2015.07.006