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General symmetric starter of orthogonal double covers of complete bipartite graph.

El-Shanawany, R.A., Higazy, M.Sh. (2007)

International Journal of Mathematics and Mathematical Sciences

Generalizations of the tree packing conjecture

Dániel Gerbner, Balázs Keszegh, Cory Palmer (2012)

Discussiones Mathematicae Graph Theory

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

Yinkui Li, Yaping Mao, Zhao Wang, Zongtian Wei (2021)

Czechoslovak Mathematical Journal

We study the generalized $k$ -connectivity $κ_{k} (G)$ as introduced by Hager in 1985, as well as the more recently introduced generalized $k$ -edge-connectivity $λ_{k} (G)$ . We determine the exact value of $κ_{k} (G)$ and $λ_{k} (G)$ for the line graphs and total graphs of trees, unicyclic graphs, and also for complete graphs for the case $k = 3$ .

Generalized list colourings of graphs

Mieczysław Borowiecki, Ewa Drgas-Burchardt, Peter Mihók (1995)

Discussiones Mathematicae Graph Theory

We prove: (1) that $c h_{P} (G) - χ_{P} (G)$ can be arbitrarily large, where $c h_{P} (G)$ and $χ_{P} (G)$ 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.

R.G. Stanton, I.P. Goulden (1981)

Aequationes mathematicae

Graph products and new solutions to Oberwolfach problems.

Rinaldi, Gloria, Traetta, Tommaso (2011)

The Electronic Journal of Combinatorics [electronic only]

Graphical condensation, overlapping Pfaffians and superpositions of matchings.

Fulmek, Markus (2010)

The Electronic Journal of Combinatorics [electronic only]

Graphs with greatest number of matchings.

I. Gutman (1980)

Publications de l'Institut Mathématique [Elektronische Ressource]

Graphs with Large Generalized (Edge-)Connectivity

Xueliang Li, Yaping Mao (2016)

Discussiones Mathematicae Graph Theory

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.

Gutman, Ivan (1983)

Publications de l'Institut Mathématique. Nouvelle Série

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