Displaying similar documents to “Minimum maximal graphs with forbidden subgraphs”

On some variations of extremal graph problems

Gabriel Semanišin (1997)

Discussiones Mathematicae Graph Theory

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A set P of graphs is termed hereditary property if and only if it contains all subgraphs of any graph G belonging to P. A graph is said to be maximal with respect to a hereditary property P (shortly P-maximal) whenever it belongs to P and none of its proper supergraphs of the same order has the property P. A graph is P-extremal if it has a the maximum number of edges among all P-maximal graphs of given order. The number of its edges is denoted by ex(n, P). If the number of edges...

Degree Sequences of Monocore Graphs

Allan Bickle (2014)

Discussiones Mathematicae Graph Theory

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A k-monocore graph is a graph which has its minimum degree and degeneracy both equal to k. Integer sequences that can be the degree sequence of some k-monocore graph are characterized as follows. A nonincreasing sequence of integers d0, . . . , dn is the degree sequence of some k-monocore graph G, 0 ≤ k ≤ n − 1, if and only if k ≤ di ≤ min {n − 1, k + n − i} and ⨊di = 2m, where m satisfies [...] ≤ m ≤ k ・ n − [...] .