Two families of chromatically unique graphs. by Yee, Hock Peng

“…In this paper, We prove that a graph (resp., a bipartite graph) obtained from K2,4 U P3 (s ≥ 3) (resp., K3,3 U P3 (s ≥ 7)) by identifying the end vertices of the path Ps with any two vertices of the complete bipartite graph K2,4 (resp., K3,3) is chromatically unique.…”
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Markov bases and toric ideals for some contingency tables by Mohammed, Nadia Faiq, Rakhimov, Isamiddin Sattarovich, Shitan, Mahendran

“…Moreover, the connected bipartite graph is also constructed by using elements of Markov basis. …”
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Heuristic factors in ant system algorithm for course timetabling problem by Djamarus, Djasli, Ku-Mahamud, Ku Ruhana

“…This paper presents an algorithm that is based on ant system to solve the course timetabling problem.The problem is modeled using the bipartite graph.Four heuristic factors are derived from the graph characteristic, are used to direct ants as the agent in finding course timetable elements The concept of negative pheromone was also applied to ensure that paths leading to dead ends are not chosen.The performance of this proposed algorithm is promising when comparison of performance was made with the original ant system algorithm. …”

A genetic algorithm to minimise the maximum lateness on a single machine family scheduling problem by Lee, Lai Soon, Nazif, Habibeh

“…During crossover, the OCGA selects two parents from the population and replaces them with two children by an optimized crossover mechanism which designed using an undirected bipartite graph. Various techniques are also introduced to further enhance the solution quality. …”