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On the basis number of the wreath product of ladders
( Charles Babbage Research Centre , 2016 , Article)The basis number of a graph G is defined to be the least non negative integer d such that there is a basis B of the cycle space of G such that each edge of G is contained in at most d members of B. In this paper, we determine ... -
The theta-complete graph Ramsey number R(θn K5) = 4n - 3 for n = 6 and n≥ 10
( Charles Babbage Research Centre , 2017 , Article)For any two graphs F1 and F2, the graph Ramsey number r(F1, F2) is the smallest positive integer N with the property that every graph of at least N vertices contains F1 or its complement contains F2 as a subgraph. In this ...