DOI: 10.5176/2251-1911_CMCGS66
Authors: Mohammad Bataineh, Mohammed Jaradat and Izdehar Al-Shboul
Abstract: In [4], Bataineh, Jaradat and Al-Shboul, gave an upper bound for the size of the edge maximal non-bipartite graphs that contains no theta graphs of order 7 and of minimum degree is at least 25. In this paper we determine the exact value of the size of the same without the constrain that the minimum degree is at least 25. Our result generalize the above result and confirm the conjecture made in [1], "Some extremal problems in graph theory", Ph.D thesis, Curtin University of Technology, Australia (2007), in case k = 3.
Keywords: Extremal graphs; edge maximal graphs; Turán’s problem; theta graphs; bipartite graphs; cycles
Updating...