Packing Trees Into n-Chromatic Graphs
We show that if a sequence of trees T1, T2, ..., Tn−1 can be packed into Kn then they can be also packed into any n-chromatic graph.
Extremal problems for forbidden pairs that imply hamiltonicity
Let C denote the claw , N the net (a graph obtained from a K₃ by attaching a disjoint edge to each vertex of the K₃), W the wounded (a graph obtained from a K₃ by attaching an edge to one vertex and a disjoint path P₃ to a second vertex), and the graph consisting of a K₃ with a path of length i attached to one vertex. For k a fixed positive integer and n a sufficiently large integer, the minimal number of edges and the smallest clique in a k-connected graph G of order n that is CY-free (does...
Fruit salad.
Vertex covering with monochromatic paths.
On -bounded families of graphs.
The Ramsey number of diamond-matchings and loose cycles in hypergraphs.
Partitioning 3-colored complete graphs into three monochromatic cycles.
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