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13,252
Cycles and paths in edgecolored graphs with given degrees
, 2007
"... We study sufficient degree conditions under various aspects guarantying the existence of properly edgecolored cycles and paths in edgecolored simple graphs, multigraphs and random graphs. In particular, we prove that an edgecolored multigraph of order n on at least three colors and with minimum c ..."
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Cited by 11 (1 self)
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We study sufficient degree conditions under various aspects guarantying the existence of properly edgecolored cycles and paths in edgecolored simple graphs, multigraphs and random graphs. In particular, we prove that an edgecolored multigraph of order n on at least three colors and with minimum
Monochromatic cycle partitions of edgecolored graphs
, 2009
"... In this paper we study the monochromatic cycle partition problem for noncomplete graphs. We consider graphs with a given independence number α(G) = α. Generalizing a classical conjecture of Erdős, Gyárfás and Pyber, we conjecture that if we rcolor the edges of a graph G with α(G) = α, then the v ..."
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Cited by 4 (1 self)
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In this paper we study the monochromatic cycle partition problem for noncomplete graphs. We consider graphs with a given independence number α(G) = α. Generalizing a classical conjecture of Erdős, Gyárfás and Pyber, we conjecture that if we rcolor the edges of a graph G with α(G) = α
Extremal Problems on Edge_Colorings, . . . CYCLE SPECTRA OF GRAPHS
, 2010
"... We study problems in extremal graph theory with respect to edgecolorings, independent sets, and cycle spectra. In Chapters 2 and 3, we present results in Ramsey theory, where we seek Ramsey host graphs with small maximum degree. In Chapter 4, we study a Ramseytype problem on edgelabeled trees, whe ..."
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We study problems in extremal graph theory with respect to edgecolorings, independent sets, and cycle spectra. In Chapters 2 and 3, we present results in Ramsey theory, where we seek Ramsey host graphs with small maximum degree. In Chapter 4, we study a Ramseytype problem on edgelabeled trees
Partitioning 2edgecolored graphs by monochromatic paths and cycles
, 2013
"... We present results on partitioning the vertices of 2edgecolored graphs into monochromatic paths and cycles. We prove asymptotically the twocolor case of a conjecture of Sárközy: the vertex set of every 2edgecolored graph can be partitioned into at most 2α(G) monochromatic cycles, where α(G) den ..."
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Cited by 2 (0 self)
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We present results on partitioning the vertices of 2edgecolored graphs into monochromatic paths and cycles. We prove asymptotically the twocolor case of a conjecture of Sárközy: the vertex set of every 2edgecolored graph can be partitioned into at most 2α(G) monochromatic cycles, where α
Long properly colored cycles in edgecolored complete graphs
, 2013
"... Let Kcn denote a complete graph on n vertices whose edges are colored in an arbitrary way. Let ∆mon(Kcn) denote the maximum number of edges of the same color incident with a vertex of Kn. A properly colored cycle (path) in Kcn is a cycle (path) in which adjacent edges have distinct colors. B. Bollob ..."
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Let Kcn denote a complete graph on n vertices whose edges are colored in an arbitrary way. Let ∆mon(Kcn) denote the maximum number of edges of the same color incident with a vertex of Kn. A properly colored cycle (path) in Kcn is a cycle (path) in which adjacent edges have distinct colors. B
On Restricted edgecolorings of bicliques
"... We investigate the minimum and maximum number of colors in edgecolorings of Kn,n such that every copy of Kp,p receives at least q and at most q ′ colors. Along the way we improve the bounds on some bipartite Turán numbers. ..."
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Cited by 2 (2 self)
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We investigate the minimum and maximum number of colors in edgecolorings of Kn,n such that every copy of Kp,p receives at least q and at most q ′ colors. Along the way we improve the bounds on some bipartite Turán numbers.
THREE EDGECOLORING CONJECTURES
"... The focus of this article is on three of the author’s open conjectures. The article itself surveys results relating to the conjectures and shows where the conjectures are known to hold. ..."
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The focus of this article is on three of the author’s open conjectures. The article itself surveys results relating to the conjectures and shows where the conjectures are known to hold.
Note on edgecolored graphs and digraphs without properly colored cycles
"... We study the following two functions: d(n, c) and d(n, c); here d(n, c) ( d(n, c)) is the minimum number k such that every cedgecolored undirected (directed) graph of order n and minimum monochromatic degree (outdegree) at least k has a properly colored cycle. Abouelaoualim et al. (2007) state ..."
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We study the following two functions: d(n, c) and d(n, c); here d(n, c) ( d(n, c)) is the minimum number k such that every cedgecolored undirected (directed) graph of order n and minimum monochromatic degree (outdegree) at least k has a properly colored cycle. Abouelaoualim et al. (2007
Properly colored subgraphs and rainbow subgraphs in edgecolorings with local constraints
 ALGORITHMS
, 2003
"... We consider a canonical Ramsey type problem. An edgecoloring of a graph is called mgood if each color appears at most m times at each vertex. Fixing a graph G and a positive integer m, let f(m, G) denote the smallest n such that every mgood edgecoloring of K n yields a properly edgecolored ..."
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Cited by 33 (1 self)
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We consider a canonical Ramsey type problem. An edgecoloring of a graph is called mgood if each color appears at most m times at each vertex. Fixing a graph G and a positive integer m, let f(m, G) denote the smallest n such that every mgood edgecoloring of K n yields a properly edgecolored
Rainbow edgecoloring and rainbow domination
, 2012
"... Let G be an edgecolored graph with n vertices. A rainbow subgraph is a subgraph whose edges have distinct colors. The rainbow edgechromatic number of G, written ˆχ ′(G), is the minimum number of rainbow matchings needed to cover E(G). An edgecolored graph is ttolerant if it contains no monochroma ..."
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Cited by 2 (2 self)
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no monochromatic star with t+1 edges. If G is ttolerant, then ˆχ ′(G) < t(t + 1)n ln n, and examples exist with ˆχ ′(G) ≥ t 2 (n − 1). The rainbow domination number, written ˆγ(G), is the minimum number of disjoint rainbow stars needed to cover V (G). For ttolerant edgecolored nvertex graphs, we generalize
Results 1  10
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13,252