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Backbone colorings along stars and matchings in split graphs: their span is close to the chromatic number

Hajo Broersma, Bert Marchal, Daniel Paulusma, A.N.M. Salman (2009)

Discussiones Mathematicae Graph Theory

We continue the study on backbone colorings, a variation on classical vertex colorings that was introduced at WG2003. Given a graph G = (V,E) and a spanning subgraph H of G (the backbone of G), a λ-backbone coloring for G and H is a proper vertex coloring V→ {1,2,...} of G in which the colors assigned to adjacent vertices in H differ by at least λ. The algorithmic and combinatorial properties of backbone colorings have been studied for various types of backbones in a number of papers. The main outcome...

Balanced Gray codes.

Bhat, Girish S., Savage, Carla D. (1996)

The Electronic Journal of Combinatorics [electronic only]

Balanced path decomposition of λ K n , n and λ K n , n *

Hung-Chih Lee, Chiang Lin (2009)

Czechoslovak Mathematical Journal

Let P k denote a path with k edges and ł K n , n denote the ł -fold complete bipartite graph with both parts of size n . In this paper, we obtain the necessary and sufficient conditions for ł K n , n to have a balanced P k -decomposition. We also obtain the directed version of this result.

Balanced problems on graphs with categorization of edges

Štefan Berežný, Vladimír Lacko (2003)

Discussiones Mathematicae Graph Theory

Suppose a graph G = (V,E) with edge weights w(e) and edges partitioned into disjoint categories S₁,...,Sₚ is given. We consider optimization problems on G defined by a family of feasible sets (G) and the following objective function: L ₅ ( D ) = m a x 1 ≤ i ≤ p ( m a x e ∈ S i ∩ D w ( e ) - m i n e ∈ S i ∩ D w ( e ) ) For an arbitrary number of categories we show that the L₅-perfect matching, L₅-a-b path, L₅-spanning tree problems and L₅-Hamilton cycle (on a Halin graph) problem are NP-complete. We also summarize polynomiality results concerning above objective functions for arbitrary...

Band combinatorics of domestic string algebras

Gena Puninski (2007)

Colloquium Mathematicae

We prove that the multiplicity of a simple module as a composition factor in a composition series for a primitive band module over a domestic string algebra is at most two.

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