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A tree is classified as being type I provided that there are two or more Perron branches at its characteristic vertex. The question arises as to how one might construct such a tree in which the Perron branches at the characteristic vertex are not isomorphic. Motivated by an example of Grone and Merris, we produce a large class of such trees, and show how to construct others from them. We also investigate some of the properties of a subclass of these trees. Throughout, we exploit connections between...

Constructions over tournaments

Jaroslav Ježek (2003)

Czechoslovak Mathematical Journal

We investigate tournaments that are projective in the variety that they generate, and free algebras over partial tournaments in that variety. We prove that the variety determined by three-variable equations of tournaments is not locally finite. We also construct infinitely many finite, pairwise incomparable simple tournaments.

Constructive lower bounds on classical multicolor Ramsey numbers.

Xu, Xiaodong, Xie, Zheng, Exoo, Geoffrey, Radziszowski, Stanisław P. (2004)

The Electronic Journal of Combinatorics [electronic only]

Constructive upper bounds for cycle-saturated graphs of minimum size.

Gould, Ronald, Łuczak, Tomasz, Schmitt, John (2006)

The Electronic Journal of Combinatorics [electronic only]

Containers and wide diameters of $P_{3} (G)$

Daniela Ferrero, Manju K. Menon, A. Vijayakumar (2012)

Mathematica Bohemica

The $P_{3}$ intersection graph of a graph $G$ has for vertices all the induced paths of order 3 in $G$ . Two vertices in $P_{3} (G)$ are adjacent if the corresponding paths in $G$ are not disjoint. A $w$ -container between two different vertices $u$ and $v$ in a graph $G$ is a set of $w$ internally vertex disjoint paths between $u$ and $v$ . The length of a container is the length of the longest path in it. The $w$ -wide diameter of $G$ is the minimum number $l$ such that there is a $w$ -container of length at most $l$ between any pair of different...

Continuation of a 3-coloring from a 7-face onto a plane graph without $C_{3}$ .

Aksenov, V.A., Borodin, O.V., Glebov, A.N. (2004)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

Continuity of the percolation threshold in randomly grown graphs.

Turova, Tatyana S. (2007)

Electronic Journal of Probability [electronic only]

Continuous monoids and yields of infinite trees

M. Dauchet, E. Timmerman (1986)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Contractible edges in some $k$ -connected graphs

Yingqiu Yang, Liang Sun (2012)

Czechoslovak Mathematical Journal

An edge $e$ of a $k$ -connected graph $G$ is said to be $k$ -contractible (or simply contractible) if the graph obtained from $G$ by contracting $e$ (i.e., deleting $e$ and identifying its ends, finally, replacing each of the resulting pairs of double edges by a single edge) is still $k$ -connected. In 2002, Kawarabayashi proved that for any odd integer $k \geq 5$ , if $G$ is a $k$ -connected graph and $G$ contains no subgraph $D = K_{1} + (K_{2} \cup K_{1, 2})$ , then $G$ has a $k$ -contractible edge. In this paper, by generalizing this result, we prove that for any integer...

Contraction distance between isomorphism classes of graphs

Bohdan Zelinka (1990)

Časopis pro pěstování matematiky

Contribution to the problem of the spectra of compound graphs.

I. Gutman (1978)

Publications de l'Institut Mathématique [Elektronische Ressource]

Control flow graphs and code coverage

Robert Gold (2010)

International Journal of Applied Mathematics and Computer Science

The control flow of programs can be represented by directed graphs. In this paper we provide a uniform and detailed formal basis for control flow graphs combining known definitions and results with new aspects. Two graph reductions are defined using only syntactical information about the graphs, but no semantical information about the represented programs. We prove some properties of reduced graphs and also about the paths in reduced graphs. Based on graphs, we define statement coverage and branch...

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Displaying 281 – 300 of 390

Constructing hypohamiltonian snarks with cyclic connectivity 5 and 6.

Constructing regular maps and graphs from planar quotients

Construction of codes identifying sets of vertices.

Construction of finite $p$ -groups with prescribed group of noncentral automorphisms

Constructions for cubic graphs with large girth.

Constructions for type I trees with nonisomorphic Perron branches