Generating Internally Four-Connected Graphs
نویسندگان
چکیده
منابع مشابه
Generating 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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A biconnected plane graph G is called internally triconnected if any cut-pair consists of outer vertices and its removal results in only components each of which contains at least one outer vertex. In a rooted plane graph, an edge is designated as an outer edge with a specified direction. For given positive integers n ≥ 1 and g ≥ 3, let G3(n, g) (resp., Gint(n, g)) denote the class of all trico...
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5 Let C = {C n : n ≥ 5} and let L = {G : G is the line graph of an internally 4-connected cubic graph}. 6 A classical result of Martinov states that every 4-connected graph G can be constructed from graphs in 7 C ∪L by repeatedly splitting vertices. In this paper we prove that, in fact, G can be constructed from C 5 8 or C 6 in the same way, unless G belongs to C ∪L. Moreover, if G is nonplanar...
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5 Archdeacon proved that projective-planar graphs are characterized by 35 excluded minors. 6 Using this result we show that internally 4-connected projective-planar graphs are characterized 7 by 23 internally 4-connected excluded minors. 8
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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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2002
ISSN: 0095-8956
DOI: 10.1006/jctb.2001.2089