General symmetric starter of orthogonal double covers of complete bipartite graph.
Generalizations of the tree packing conjecture
The Gyárfás tree packing conjecture asserts that any set of trees with 2,3,...,k vertices has an (edge-disjoint) packing into the complete graph on k vertices. Gyárfás and Lehel proved that the conjecture holds in some special cases. We address the problem of packing trees into k-chromatic graphs. In particular, we prove that if all but three of the trees are stars then they have a packing into any k-chromatic graph. We also consider several other generalizations of the conjecture.
Generalized connectivity of some total graphs
We study the generalized -connectivity as introduced by Hager in 1985, as well as the more recently introduced generalized -edge-connectivity . We determine the exact value of and for the line graphs and total graphs of trees, unicyclic graphs, and also for complete graphs for the case .
Generalized list colourings of graphs
We prove: (1) that can be arbitrarily large, where and are P-choice and P-chromatic numbers, respectively, (2) the (P,L)-colouring version of Brooks’ and Gallai’s theorems.
Graph factorization, general triple systems, and cyclic triple systems.
Graph products and new solutions to Oberwolfach problems.
Graphical condensation, overlapping Pfaffians and superpositions of matchings.
Graphs with greatest number of matchings.
Graphs with Large Generalized (Edge-)Connectivity
The generalized k-connectivity κk(G) of a graph G, introduced by Hager in 1985, is a nice generalization of the classical connectivity. Recently, as a natural counterpart, we proposed the concept of generalized k-edge-connectivity λk(G). In this paper, graphs of order n such that [...] for even k are characterized.
Graphs with maximum and minimum independence numbers.