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More on even [a,b]-factors in graphs

Abdollah Khodkar, Rui Xu (2007)

Discussiones Mathematicae Graph Theory

In this note we give a characterization of the complete bipartite graphs which have an even (odd) [a,b]-factor. For general graphs we prove that an a-edge connected graph G with n vertices and with δ(G) ≥ max{a+1,an/(a+b) + a - 2} has an even [a,b]-factor, where a and b are even and 2 ≤ a ≤ b. With regard to the edge-connectivity this result is slightly better than one of the similar results obtained by Kouider and Vestergaard in 2004 and unlike their results, this result has no restriction on the...

Network tomography.

Berenstein, Carlos A., Gavilánez, Franklin (2007)

Revista Colombiana de Matemáticas

Note on a Lovász's result

Dănuţ Marcu (1997)

Mathematica Bohemica

In this paper, we give a generalization of a result of Lovasz from [2].

Note on graphs colouring

Dănuţ Marcu (1992)

Mathematica Bohemica

In this paper, we show that the maximal number of minimal colourings of a graph with n vertices and the chromatic number k is equal to k n - k , and the single graph for which this bound is attained consists of a k -clique and n - k isolated vertices.

Note on k -chromatic graphs

Dănuţ Marcu (1994)

Mathematica Bohemica

In this paper we characterize k -chromatic graphs without isolated vertices and connected k -chromatic graphs having a minimal number of edges.

On a bound on algebraic connectivity: the case of equality

Stephen J. Kirkland, Neumann, Michael, Bryan L. Shader (1998)

Czechoslovak Mathematical Journal

In a recent paper the authors proposed a lower bound on 1 - λ i , where λ i , λ i ≠ 1 , is an eigenvalue of a transition matrix T of an ergodic Markov chain. The bound, which involved the group inverse of I - T , was derived from a more general bound, due to Bauer, Deutsch, and Stoer, on the eigenvalues of a stochastic matrix other than its constant row sum. Here we adapt the bound to give a lower bound on the algebraic connectivity of an undirected graph, but principally consider the case of equality in the bound when...

On connected resolving decompositions in graphs

Varaporn Saenpholphat, Ping Zhang (2004)

Czechoslovak Mathematical Journal

For an ordered k -decomposition 𝒟 = { G 1 , G 2 , ⋯ , G k } of a connected graph G and an edge e of G , the 𝒟 -code of e is the k -tuple c 𝒟 ( e ) = ( d ( e , G 1 ) , d ( e , G 2 ) , ... , d ( e , G k ) ) , where d ( e , G i ) is the distance from e to G i . A decomposition 𝒟 is resolving if every two distinct edges of G have distinct 𝒟 -codes. The minimum k for which G has a resolving k -decomposition is its decomposition dimension dim d ( G ) . A resolving decomposition 𝒟 of G is connected if each G i is connected for 1 ≤ i ≤ k . The minimum k for which G has a connected resolving k -decomposition is its connected decomposition...

On distance local connectivity and vertex distance colouring

Přemysl Holub (2007)

Discussiones Mathematicae Graph Theory

In this paper, we give some sufficient conditions for distance local connectivity of a graph, and a degree condition for local connectivity of a k-connected graph with large diameter. We study some relationships between t-distance chromatic number and distance local connectivity of a graph and give an upper bound on the t-distance chromatic number of a k-connected graph with diameter d.

Currently displaying 101 – 120 of 199