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For a connected graph G, the r-th extraconnectivity κ r (G) is defined as the minimum cardinality of a cutset X such that all remaining components after the deletion of the vertices of X have at least r+1 vertices. The standard connectivity and superconnectivity correspond to κ 0 (G) and κ 1 (G), respectively. The minimum r-tree degree of G, denoted by ξ r… (More)

Girth pairs were introduced by Harary and Kovács [Regular graphs with given girth pair, J. Graph Theory 7 (1983) 209–218]. The odd girth (even girth) of a graph is the length of a shortest odd (even) cycle. Let g denote the smaller of the odd and even girths, and let h denote the larger. Then (g, h) is called the girth pair of the graph. In this paper we… (More)

The extremal number ex(n; MK p) denotes the maximum number of edges of a graph of order n containing no complete graph K p as a minor. In this paper we give the exact value of the extremal number ex(n; MK p) for (5n + 9)/8 p (2n − 1)/3 provided that n − p 24. Indeed we show that this number is the size of the Turán Graph T 2p−n−1 (n) and this graph is the… (More)