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Displaying 201 – 220 of 238

Some graphic uses of an even number of odd nodes

Kathie Cameron, Jack Edmonds (1999)

Annales de l'institut Fourier

Vertex-degree parity in large implicit “exchange graphs” implies some EP theorems asserting the existence of a second object without evidently providing a polytime algorithm for finding a second object.

Some new results about the shortness exponent in polyhedral graphs

Jochen Harant, Hansjoachim Walther (1987)

Časopis pro pěstování matematiky

Some properties of the zero divisor graph of a commutative ring

Khalida Nazzal, Manal Ghanem (2014)

Discussiones Mathematicae - General Algebra and Applications

Let Γ(R) be the zero divisor graph for a commutative ring with identity. The k-domination number and the 2-packing number of Γ(R), where R is an Artinian ring, are computed. k-dominating sets and 2-packing sets for the zero divisor graph of the ring of Gaussian integers modulo n, Γ(ℤₙ[i]), are constructed. The center, the median, the core, as well as the automorphism group of Γ(ℤₙ[i]) are determined. Perfect zero divisor graphs Γ(R) are investigated.

Some remarks on Eulerian graphs

Bohdan Zelinka (1979)

Czechoslovak Mathematical Journal

Some remarks on Jaeger's dual-hamiltonian conjecture

Bill Jackson, Carol A. Whitehead (1999)

Annales de l'institut Fourier

François Jaeger conjectured in 1974 that every cyclically 4-connected cubic graph $G$ is dual hamiltonian, that is to say the vertices of $G$ can be partitioned into two subsets such that each subset induces a tree in $G$ . We shall make several remarks on this conjecture.

Squares of triangular cacti

Stanislav Říha, Milan Sekanina (1983)

Archivum Mathematicum

Strongly pancyclic and dual-pancyclic graphs

Terry A. McKee (2009)

Discussiones Mathematicae Graph Theory

Say that a cycle C almost contains a cycle C¯ if every edge except one of C¯ is an edge of C. Call a graph G strongly pancyclic if every nontriangular cycle C almost contains another cycle C¯ and every nonspanning cycle C is almost contained in another cycle C⁺. This is equivalent to requiring, in addition, that the sizes of C¯ and C⁺ differ by one from the size of C. Strongly pancyclic graphs are pancyclic and chordal, and their cycles enjoy certain interpolation and extrapolation properties with...

Subsemi-Eulerian graphs.

Suffel, Charles, Tindell, Ralph, Hoffman, Cynthia, Mandell, Manachem (1982)

International Journal of Mathematics and Mathematical Sciences

Symmetric Hamilton Cycle Decompositions of Complete Multigraphs

V. Chitra, A. Muthusamy (2013)

Discussiones Mathematicae Graph Theory

Let n ≥ 3 and ⋋ ≥ 1 be integers. Let ⋋Kn denote the complete multigraph with edge-multiplicity ⋋. In this paper, we show that there exists a symmetric Hamilton cycle decomposition of ⋋K2m for all even ⋋ ≥ 2 and m ≥ 2. Also we show that there exists a symmetric Hamilton cycle decomposition of ⋋K2m − F for all odd ⋋ ≥ 3 and m ≥ 2. In fact, our results together with the earlier results (by Walecki and Brualdi and Schroeder) completely settle the existence of symmetric Hamilton cycle decomposition of...

The Chvátal-Erdős condition and 2-factors with a specified number of components

Guantao Chen, Ronald J. Gould, Ken-ichi Kawarabayashi, Katsuhiro Ota, Akira Saito, Ingo Schiermeyer (2007)

Discussiones Mathematicae Graph Theory

Let G be a 2-connected graph of order n satisfying α(G) = a ≤ κ(G), where α(G) and κ(G) are the independence number and the connectivity of G, respectively, and let r(m,n) denote the Ramsey number. The well-known Chvátal-Erdös Theorem states that G has a hamiltonian cycle. In this paper, we extend this theorem, and prove that G has a 2-factor with a specified number of components if n is sufficiently large. More precisely, we prove that (1) if n ≥ k·r(a+4, a+1), then G has a 2-factor with k components,...

The flower conjecture in special classes of graphs

Zdeněk Ryjáček, Ingo Schiermeyer (1995)

Discussiones Mathematicae Graph Theory

We say that a spanning eulerian subgraph F ⊂ G is a flower in a graph G if there is a vertex u ∈ V(G) (called the center of F) such that all vertices of G except u are of the degree exactly 2 in F. A graph G has the flower property if every vertex of G is a center of a flower. Kaneko conjectured that G has the flower property if and only if G is hamiltonian. In the present paper we prove this conjecture in several special classes of graphs, among others in squares and in a certain...

The full periodicity kernel for a class of graph maps.

Alsedá, Ll., Paraños, J., Rodriguez, J.A. (1997)

Acta Mathematica Universitatis Comenianae. New Series

The hamiltonian chromatic number of a connected graph without large hamiltonian-connected subgraphs

Ladislav Nebeský (2006)

Czechoslovak Mathematical Journal

If $G$ is a connected graph of order $n \geq 1$ , then by a hamiltonian coloring of $G$ we mean a mapping $c$ of $V (G)$ into the set of all positive integers such that $| c (x) - c (y) | \geq n - 1 - D_{G} (x, y)$ (where $D_{G} (x, y)$ denotes the length of a longest $x - y$ path in $G$ ) for all distinct $x, y \in V (G)$ . Let $G$ be a connected graph. By the hamiltonian chromatic number of $G$ we mean $min (max (c (z); z \in V (G))),$ where the minimum is taken over all hamiltonian colorings $c$ of $G$ . The main result of this paper can be formulated as follows: Let $G$ be a connected graph of order $n \geq 3$ . Assume that there exists a subgraph...

The number of knight's tours equals 33, 439, 123, 484, 294—counting with binary decision diagrams.

Loebbing, Martin, Wegener, Ingo (1996)

The Electronic Journal of Combinatorics [electronic only]

The prism of the acyclic orientation graph is Hamiltonian.

Pruesse, Gara, Ruskey, Frank (1995)

The Electronic Journal of Combinatorics [electronic only]

The Ryjáček Closure and a Forbidden Subgraph

Akira Saito, Liming Xiong (2016)

Discussiones Mathematicae Graph Theory

The Ryjáček closure is a powerful tool in the study of Hamiltonian properties of claw-free graphs. Because of its usefulness, we may hope to use it in the classes of graphs defined by another forbidden subgraph. In this note, we give a negative answer to this hope, and show that the claw is the only forbidden subgraph that produces non-trivial results on Hamiltonicity by the use of the Ryjáček closure.

The signed k-domination number of directed graphs

Maryam Atapour, Seyyed Sheikholeslami, Rana Hajypory, Lutz Volkmann (2010)

Open Mathematics

The upper traceable number of a graph

Futaba Okamoto, Ping Zhang, Varaporn Saenpholphat (2008)

Czechoslovak Mathematical Journal

For a nontrivial connected graph $G$ of order $n$ and a linear ordering $s v_{1}, v_{2}, ..., v_{n}$ of vertices of $G$ , define $d (s) = \sum_{i = 1}^{n - 1} d (v_{i}, v_{i + 1})$ . The traceable number $t (G)$ of a graph $G$ is $t (G) = min {d (s)}$ and the upper traceable number $t^{+} (G)$ of $G$ is $t^{+} (G) = max {d (s)},$ where the minimum and maximum are taken over all linear orderings $s$ of vertices of $G$ . We study upper traceable numbers of several classes of graphs and the relationship between the traceable number and upper traceable number of a graph. All connected graphs $G$ for which $t^{+} (G) - t (G) = 1$ are characterized and a formula for the upper...

Three-linking in Eulerian digraphs

Toshihide Ibaraki, Svatopluk Poljak (1989)

Commentationes Mathematicae Universitatis Carolinae

Topological circles and Euler tours in locally finite graphs.

Georgakopoulos, Agelos (2009)

The Electronic Journal of Combinatorics [electronic only]

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