Colourings in Bipartite graphs
Yanamandram Balasubramanian Venkatakrishnan, V. Swaminathan · International Journal of Computer Applications · 2011
The concept of X-chromatic partition and hyper independent chromatic partition of bipartite graphs were introduced by Stephen Hedetniemi and Renu Laskar.We find the bounds for X-chromatic number and hyper independent chromatic number of a bipartite graph.The existence of bipartite graph with χ h (G)=a and γ Y (G)=b-1, χ h (G)=a and χ X (G)=b where a ≤b are proved.We also prove the existence of bipartite graphs for any three positive integers a, b, c such that c ≥ 2(b-a)+1, there exists a graph G such that χ X (G)=a, χ X d(G)=b and |Y|=c.The bipartite theory of Dominator colouring is introduced.