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217,388
Finding Odd Cycle Transversals
, 2003
"... We present an O(mn) algorithm to determine whether a graph G with m edges and n vertices has an odd cycle cover of order at most k, for any fixed k. We also obtain an algorithm that determines, in the same time, whether a graph has a half integral packing of odd cycles of weight k. ..."
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Cited by 97 (2 self)
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We present an O(mn) algorithm to determine whether a graph G with m edges and n vertices has an odd cycle cover of order at most k, for any fixed k. We also obtain an algorithm that determines, in the same time, whether a graph has a half integral packing of odd cycles of weight k.
Graph homomorphism into an odd cycle
"... For integers n> k ≥ 4, a simple graph with n vertices that contains no odd cycle of length at most 2k − 1 and that has minimum degree exceeding ..."
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Cited by 2 (0 self)
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For integers n> k ≥ 4, a simple graph with n vertices that contains no odd cycle of length at most 2k − 1 and that has minimum degree exceeding
Odd cycles in planar graphs
, 2005
"... Given a graph G = (V,E), an odd cycle cover is a subset of the vertices whose removal makes the graph bipartite, that is, it meets all odd cycles in G. A packing in G is a collection of vertex disjoint odd cycles. This thesis addresses algorithmic and structural problems concerning odd cycle covers ..."
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Cited by 2 (1 self)
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Given a graph G = (V,E), an odd cycle cover is a subset of the vertices whose removal makes the graph bipartite, that is, it meets all odd cycles in G. A packing in G is a collection of vertex disjoint odd cycles. This thesis addresses algorithmic and structural problems concerning odd cycle covers
The biased odd cycle game
"... In this paper we consider biased MakerBreaker games played on the edge set of a given graph G. We prove that for every δ> 0 and large enough n, there exists a constant k for which if δ(G) ≥ δn and χ(G) ≥ k, then Maker can build an odd cycle in the (1: b) game for b = O n log 2 n. We also consi ..."
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In this paper we consider biased MakerBreaker games played on the edge set of a given graph G. We prove that for every δ> 0 and large enough n, there exists a constant k for which if δ(G) ≥ δn and χ(G) ≥ k, then Maker can build an odd cycle in the (1: b) game for b = O n log 2 n. We also
HAT PROBLEM ON ODD CYCLES
, 2011
"... The topic is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one gue ..."
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Cited by 2 (2 self)
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several results that support this conjecture, and solved the hat problem for bipartite graphs and planar graphs containing a triangle. We make a step towards proving the conjecture of Feige. We solve the hat problem on all cycles of odd length. Of course, the maximum chance of success for the hat problem
Multipartite Ramsey numbers for odd cycles
, 2007
"... In this paper we study multipartite Ramsey numbers for odd cycles. We formulate the following conjecture: Let n ≥ 5 be an arbitrary positive odd integer, then in any twocoloring of the edges of the complete 5partite graph ..."
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Cited by 1 (0 self)
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In this paper we study multipartite Ramsey numbers for odd cycles. We formulate the following conjecture: Let n ≥ 5 be an arbitrary positive odd integer, then in any twocoloring of the edges of the complete 5partite graph
Cobounding odd cycle colorings
, 2006
"... Abstract. We give a very short selfcontained combinatorial proof of the BabsonKozlov conjecture, by presenting a cochain whose coboundary is the desired power of the characteristic class. 1. Preliminaries The study of the following family of complexes has recently been undertaken in connection wit ..."
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Cited by 3 (1 self)
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Abstract. We give a very short selfcontained combinatorial proof of the BabsonKozlov conjecture, by presenting a cochain whose coboundary is the desired power of the characteristic class. 1. Preliminaries The study of the following family of complexes has recently been undertaken in connection with equivariant obstructions to graph colorings. Definition 1.1. For any graphs T and G, Hom(T, G) ⊆ ∏ x∈V (T) ∆V (G) consists of all cells σ = ∏ x∈V (T) σx, such that for any x, y ∈ V (T), if (x, y) ∈ E(T), then (σx, σy) is a complete bipartite subgraph of G. V (G) In particular, the cells of Hom(T, G) are indexed by functions σ: V (T) → 2 satisfying that additional property, and dimσ = ∑ v∈V (T)
On the Independence Numbers of the Cubes of Odd Cycles
, 2008
"... Abstract We give an upper bound on the independence number of the cube of the odd cycle C8n+5. The best known lower bound is conjectured to be the truth; we prove theconjecture in the case 8 n + 5 prime and, within 2, for general n. The proof of the upperbound uses a stability result for independent ..."
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Abstract We give an upper bound on the independence number of the cube of the odd cycle C8n+5. The best known lower bound is conjectured to be the truth; we prove theconjecture in the case 8 n + 5 prime and, within 2, for general n. The proof of the upperbound uses a stability result
Graphs with odd cycle lengths 5 and . . .
, 2009
"... Let L(G) denote the set of all odd cycle lengths of a graph G. Gyárfás gave an upper bound for χ(G) depending on the size of this set: if L(G)  = k ≥ 1, then χ(G) ≤ 2k +1 unless some block of G is a K2k+2, in which case χ(G) = 2k +2. This bound is generally tight, but when investigating L(G) of ..."
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Let L(G) denote the set of all odd cycle lengths of a graph G. Gyárfás gave an upper bound for χ(G) depending on the size of this set: if L(G)  = k ≥ 1, then χ(G) ≤ 2k +1 unless some block of G is a K2k+2, in which case χ(G) = 2k +2. This bound is generally tight, but when investigating L
Results 1  10
of
217,388