The number of removable edges in a 4-connected graph
نویسندگان
چکیده
Let G be a 4-connected graph. For an edge e of G; we do the following operations on G: first, delete the edge e from G; resulting the graph G e; second, for all the vertices x of degree 3 in G e; delete x from G e and then completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we use single edges to replace them. The final resultant graph is denoted by G~e: If G~e is still 4-connected, then e is called a removable edge of G: In this paper we prove that every 4-connected graph of order at least six (excluding the 2-cyclic graph of order six) has at least ð4jGj þ 16Þ=7 removable edges. We also give the structural characterization of 4-connected graphs for which the lower bound is sharp. r 2004 Elsevier Inc. All rights reserved. MSC: 05C40; 05C38; 05C75
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عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 92 شماره
صفحات -
تاریخ انتشار 2004