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On the pathavoidance vertexcoloring game
 In preparation
"... For any graph F and any integer r ≥ 2, the online vertexRamsey density of F and r, denoted m ∗ (F, r), is a parameter defined via a deterministic twoplayer Ramseytype game (Painter vs. Builder). This parameter was introduced in a recent paper [4], where it was shown that the online vertexRamsey ..."
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Cited by 2 (2 self)
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For any graph F and any integer r ≥ 2, the online vertexRamsey density of F and r, denoted m ∗ (F, r), is a parameter defined via a deterministic twoplayer Ramseytype game (Painter vs. Builder). This parameter was introduced in a recent paper [4], where it was shown that the online vertex
Online vertexcoloring games in random graphs
 Combinatorica
, 2010
"... Abstract. Consider the following oneplayer game. The vertices of a random graph on n vertices are revealed to the player one by one. In each step, also all edges connecting the newly revealed vertex to preceding vertices are revealed. The player has a fixed number of colors at her disposal, and has ..."
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Cited by 3 (2 self)
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Abstract. Consider the following oneplayer game. The vertices of a random graph on n vertices are revealed to the player one by one. In each step, also all edges connecting the newly revealed vertex to preceding vertices are revealed. The player has a fixed number of colors at her disposal
AVOIDING RAINBOW INDUCED SUBGRAPHS IN VERTEXCOLORINGS
"... Abstract. For a fixed graph H on k vertices, and a graph G on at least k vertices, we write G − → H if in any vertexcoloring of G with k colors, there is an induced subgraph isomorphic to H whose vertices have distinct colors. In other words, if G − → H then a totally multicolored induced copy of H ..."
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Cited by 2 (0 self)
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Abstract. For a fixed graph H on k vertices, and a graph G on at least k vertices, we write G − → H if in any vertexcoloring of G with k colors, there is an induced subgraph isomorphic to H whose vertices have distinct colors. In other words, if G − → H then a totally multicolored induced copy
Maximum motif problem in vertexcolored graphs
 In Proc. 20th CPM, volume 5577 of LNCS
, 2009
"... Abstract. Searching for motifs in graphs has become a crucial problem in the analysis of biological networks. In this context, different graph motif problems have been considered [12, 6, 4]. Pursuing a line of research pioneered by Lacroix et al. [12], we introduce in this paper a new graph motif pr ..."
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Cited by 7 (1 self)
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problem: given a vertex colored graph G and a motif M, where a motif is a multiset of colors, find a maximum cardinality submotif M ′ ⊆ M that occurs as a connected motif in G. We prove that the problem is APXhard even in the case where the target graph is a tree of maximum degree 3, the motif
Finding and Counting VertexColored Subtrees
 INTERNATIONAL SYMPOSIUM ON MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE (MFCS), BRNO: CZECH REPUBLIC
, 2010
"... The problems studied in this article originate from the Graph Motif problem introduced by Lacroix et al. [17] in the context of biological networks. The problem is to decide if a vertexcolored graph has a connected subgraph whose colors equal a given multiset of colors M. Using an algebraic framewo ..."
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Cited by 8 (2 self)
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The problems studied in this article originate from the Graph Motif problem introduced by Lacroix et al. [17] in the context of biological networks. The problem is to decide if a vertexcolored graph has a connected subgraph whose colors equal a given multiset of colors M. Using an algebraic
Sharp Tractability Borderlines for Finding Connected Motifs in VertexColored Graphs
 34TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP 2007), WROCLAW: POLAND
, 2007
"... We study the problem of finding occurrences of motifs in vertexcolored graphs, where a motif is a multiset of colors, and an occurrence of a motif is a subset of connected vertices with a bijection between its colors and the colors of the motif. This problem has applications in metabolic network an ..."
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Cited by 18 (8 self)
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We study the problem of finding occurrences of motifs in vertexcolored graphs, where a motif is a multiset of colors, and an occurrence of a motif is a subset of connected vertices with a bijection between its colors and the colors of the motif. This problem has applications in metabolic network
Upper and Lower Bounds for Finding Connected Motifs in VertexColored Graphs
, 2010
"... We study the problem of finding occurrences of motifs in vertexcolored graphs, where a motif is a multiset of colors, and an occurrence of a motif is a subset of connected vertices whose multiset of colors equals the motif. This problem is a natural graphtheoretic pattern matching variant where we ..."
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Cited by 11 (3 self)
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We study the problem of finding occurrences of motifs in vertexcolored graphs, where a motif is a multiset of colors, and an occurrence of a motif is a subset of connected vertices whose multiset of colors equals the motif. This problem is a natural graphtheoretic pattern matching variant where
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Complexity Issues in VertexColored Graph Pattern Matching
, 2010
"... Searching for motifs in graphs has become a crucial problem in the analysis of biological networks. In the context of metabolic network analysis, Lacroix et al [V. Lacroix, C.G. Fernandes and M.F. Sagot, IEEE/ACM Transactions on Computational Biology and Bioinformatics, 3 (2006), no. 4, 360368] int ..."
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Cited by 4 (1 self)
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] introduced the NPhard general problem of finding occurrences of motifs in vertexcolored graphs, where a motif M is a multiset of colors and an occurrence of M in a vertexcolored graph G, called the target graph, is a subset of vertices that induces a connected graph and the multiset of colors induces
VertexColored Graphs, Bicycle Spaces and Mahler Measure
, 2014
"... The space C of conservative vertex colorings (over a field F) of a countably locallyfinite graph G is introduced. The subspace C0 of based colorings is shown to be isomorphic to the bicycle space of the graph. For graphs G with a free Zdaction by automorphisms, C is a finitely generated module ove ..."
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The space C of conservative vertex colorings (over a field F) of a countably locallyfinite graph G is introduced. The subspace C0 of based colorings is shown to be isomorphic to the bicycle space of the graph. For graphs G with a free Zdaction by automorphisms, C is a finitely generated module
Results 1  10
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