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Dually vertexoblique graphs
"... A vertex with neighbours of degrees d1 ≥ · · · ≥ dr has vertex type (d1,...,dr). A graph is vertexoblique if each vertex has a distinct vertextype. While no graph can have distinct degrees, Schreyer, Walther and Mel’nikov [Vertex oblique graphs, same proceedings] have constructed infinite clas ..."
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A vertex with neighbours of degrees d1 ≥ · · · ≥ dr has vertex type (d1,...,dr). A graph is vertexoblique if each vertex has a distinct vertextype. While no graph can have distinct degrees, Schreyer, Walther and Mel’nikov [Vertex oblique graphs, same proceedings] have constructed infinite
VertexPancyclicity of
, 2007
"... Abstract: A hypertournament or a ktournament, on n vertices, 2kn, is a pair TD (V;E), where the vertex setV is a set of size n and the edge setE is the collection of all possible subsets of size k of V, called the edges, each taken in one of its k! possible permutations. A ktournament is pancyclic ..."
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tournament is pancyclic if there exists (directed) cycles of all possible lengths; it is vertexpancyclic if moreover the cycles can be found through any vertex. A ktournament is strong if there is a path from u to v for each pair of distinct vertices u and v. A question posed by Gutin and Yeo about the characterization
The Complexity of Stochastic Games
 Information and Computation
, 1992
"... We consider the complexity of stochastic games  simple games of chance played by two players. We show that the problem of deciding which player has the greatest chance of winning the game is in the class NP " coNP. 1 Introduction We consider the complexity of a natural combinatorial problem ..."
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Cited by 206 (2 self)
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, we assume that all vertices have exactly two (not necessarily distinct) neighbors, except for the sink vertices, which have no neighbors. The graph models a game between two players, 0 and 1. In the game, a token is initially placed on the start vertex, and at each step of the game the token is moved
ON VERTEX, EDGE, AND VERTEXEDGE RANDOM GRAPHS
, 2008
"... We consider three classes of random graphs: edge random graphs, vertex random graphs, and vertexedge random graphs. Edge random graphs are ErdősRényi random graphs [5, 6], vertex random graphs are generalizations of geometric random graphs [16], and vertexedge random graphs generalize both. The ..."
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Cited by 1 (1 self)
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We consider three classes of random graphs: edge random graphs, vertex random graphs, and vertexedge random graphs. Edge random graphs are ErdősRényi random graphs [5, 6], vertex random graphs are generalizations of geometric random graphs [16], and vertexedge random graphs generalize both
Vertex distinguishing colorings of graphs with
 G) = 2, Discrete Mathematics 252(2002)17 ∼ 29
"... In a paper by Burris and Schelp [3], a conjecture was made concerning the number of colors χ′s(G) required to proper edgecolor G so that each vertex has a distinct set of colors incident to it. We consider the case when ∆(G) = 2, so that G is a union of paths and cycles. In particular we find the ..."
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Cited by 10 (2 self)
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In a paper by Burris and Schelp [3], a conjecture was made concerning the number of colors χ′s(G) required to proper edgecolor G so that each vertex has a distinct set of colors incident to it. We consider the case when ∆(G) = 2, so that G is a union of paths and cycles. In particular we find
Counting OneVertex Maps ∗
, 2008
"... The number of distinct maps (premaps) with a single vertex and valence d is computed for any value of d. The types of maps (premaps) that we consider depend on whether the underlaying graph (pregraph) is signed or unsigned and directed or undirected. 1 ..."
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The number of distinct maps (premaps) with a single vertex and valence d is computed for any value of d. The types of maps (premaps) that we consider depend on whether the underlaying graph (pregraph) is signed or unsigned and directed or undirected. 1
Vertexpancyclicity of hypertournaments
 J. Graph Theory
"... Let V be a nset (set of size n). Let E be the collection of all possible ksubsets (subsets of size k) of V, 2 k n, each taken in one of its k! possible permutations. A pair T = (V; E) is called a hypertournament, or a ktournament. Each element of V is a vertex, and each ordered ktuple of E is ..."
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Let V be a nset (set of size n). Let E be the collection of all possible ksubsets (subsets of size k) of V, 2 k n, each taken in one of its k! possible permutations. A pair T = (V; E) is called a hypertournament, or a ktournament. Each element of V is a vertex, and each ordered ktuple of E
Vertextransitive CIS graphs
, 2014
"... A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. A graph is wellcovered if all its maximal stable sets are of the same size, cowellcovered if its complement is wellcovered, and vertextransitive if, for every pair of vertices, there exists an automorph ..."
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an automorphism of the graph mapping one to the other. We show that a vertextransitive graph is CIS if and only if it is wellcovered, cowellcovered, and the product of its clique and stability numbers equals its order. A graph is irreducible if no two distinct vertices have the same neighborhood. We classify
Mappings Associated with Vertex Triangles
"... Abstract. Methods of linear algebra are applied to triangle geometry. The vertex triangle of distinct circumcevian triangles is proved to be perspective to the reference triangle ABC, and similar results hold for three other classes of vertex triangles. Homogeneous coordinates of the perspectors d ..."
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Abstract. Methods of linear algebra are applied to triangle geometry. The vertex triangle of distinct circumcevian triangles is proved to be perspective to the reference triangle ABC, and similar results hold for three other classes of vertex triangles. Homogeneous coordinates of the perspectors
On Distinct Distances from a Vertex of a Convex Polygon
"... Given a set P of n points in convex position in the plane, we prove that there exists a point p 2 P such that the number of distinct distances from p is at least d(13n  6)/36e. The best previous bound, dn=3e, from 1952, is due to Leo Moser. ..."
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Cited by 5 (1 self)
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Given a set P of n points in convex position in the plane, we prove that there exists a point p 2 P such that the number of distinct distances from p is at least d(13n  6)/36e. The best previous bound, dn=3e, from 1952, is due to Leo Moser.
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