Removable edges on a Hamilton cycle or outside a cycle in a 4-connected graph
نویسندگان
چکیده
منابع مشابه
Removable edges in a cycle of a 4-connected graph
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 a e. If G a...
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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 st...
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An edge e of a k-connected graph G is said to be a removable edge if G a e is still k-connected, where Ga e denotes the graph obtained from G by deleting e to get G− e and, for any end vertex of e with degree k− 1 in G− e, say x, deleting x and then adding edges between any pair of non-adjacent vertices in NG−e(x). Xu and Guo [28] proved that a 5-connected graph G has no removable edge if and o...
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We show that the threshold for the random graph Gn,p to contain the square of a Hamilton cycle is p = 1 √ n . This improves the previous results of Kühn and Osthus and also Nenadov and Škorić.
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We show that p = √ e n is a sharp threshold for the random graph Gn,p to contain the square of a Hamilton cycle. This improves the previous results of Kühn and Osthus and also Nenadov and Škorić.
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2021
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2209