# ON MONOCHROMATIC PATHS AND BICOLORED SUBDIGRAPHS IN ARC-COLORED TOURNAMENTS

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Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is 3-transitive if the existence of the directed path (u; v;w; x) of length 3 in D implies the existence of the arc (u, x) âˆˆ A(D). In this article strong 3-transitive digraphs are...

- KERNELS BY MONOCHROMATIC PATHS AND THE COLOR-CLASS DIGRAPH. GALEANA-SÁNCHEZ, HORTENSIA // Discussiones Mathematicae: Graph Theory;2011, Vol. 31 Issue 2, p273
No abstract available.

- MONOCHROMATIC CYCLES AND MONOCHROMATIC PATHS IN ARC-COLORED DIGRAPHS. GALEANA-SÁNCHEZ, HORTENSIA; GAYTÁN-GÓMEZ, GUADALUPE; ROJAS-MONROY, ROCÍO // Discussiones Mathematicae: Graph Theory;2011, Vol. 31 Issue 2, p283
No abstract available.

- HAMILTONIAN-COLORED POWERS OF STRONG DIGRAPHS. JOHN, GARRY; JONES, RYAN; KOLASINSKI, KYLE; ZHANG, PING // Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 4, p705
For a strong oriented graph D of order n and diameter d and an integer k with 1â‰¤ k â‰¤ d, the kth power Dk of D is that digraph having vertex set V(D) with the property that (u, v) is an arc of Dk if the directed distance dD(u, v) from u to v in D is at most k. For every strong digraph...

- Game-perfect digraphs. Andres, Stephan // Mathematical Methods of Operations Research;Dec2012, Vol. 76 Issue 3, p321
In the A-coloring game, two players, Alice and Bob, color uncolored vertices of a given uncolored digraph D with colors from a given color set C, so that, at any time a vertex is colored, its color has to be different from the colors of its previously colored in-neighbors. Alice begins. The...

- Linear and 2-Frugal Choosability of Graphs of Small Maximum Average Degree. Cohen, Nathann; Havet, Fr�d�ric // Graphs & Combinatorics;Nov2011, Vol. 27 Issue 6, p831
A proper vertex colouring of a graph G is 2- frugal (resp. linear) if the graph induced by the vertices of any two colour classes is of maximum degree 2 (resp. is a forest of paths). A graph G is 2- frugally (resp. linearly) L- colourable if for a given list assignment $${L:V(G)\mapsto...

- Acyclic 5-choosability of planar graphs without 4-cycles. Borodin, O.; Ivanova, A. // Siberian Mathematical Journal;May2011, Vol. 52 Issue 3, p411
The conjecture on the acyclic 5-choosability of planar graphs (Borodin et al., 2002) as yet has been verified only for several restricted classes of graphs: those of girth at least 5 (Montassier, Ochem, and Raspaud, 2006), without 4- and 5-cycles or without 4- and 6-cycles (Montassier, Raspaud,...

- A Note on Heterochromatic C in Edge-Colored Triangle-Free Graphs. Wang, Guanghui; Li, Hao; Zhu, Yan; Liu, Guizhen // Graphs & Combinatorics;Nov2012, Vol. 28 Issue 6, p901
Let G be an edge-colored graph. A heterochromatic cycle of G is a cycle in which any pair of edges have distinct colors. Let d( v), named the color degree of a vertex v, be defined as the maximum number of edges incident with v, that have distinct colors. In this paper, we prove that if G is an...

- An Algorithm to Detect Cycle in an Undirected Graph. Kumar, Anand; Jani, N. N. // International Journal of Computational Intelligence Research;2010, Vol. 6 Issue 2, p305
This paper presents a novel algorithm to detect cycles in a graph. The graph may be of any type. Cycles are available in a graph and in much real life application; it is required to know the existence of cycles in a graph. This algorithm is developed in the context of network design problem but...