
Short rainbow cycles in sparse graphs
Let G be a simple nvertex graph and c be a colouring of E(G) with n col...
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S_12 and P_12colorings of cubic graphs
If G and H are two cubic graphs, then an Hcoloring of G is a proper edg...
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Linearly χBounding (P_6,C_4)Free Graphs
Given two graphs H_1 and H_2, a graph G is (H_1,H_2)free if it contains...
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VizingGoldberg type bounds for the equitable chromatic number of block graphs
An equitable coloring of a graph G is a proper vertex coloring of G such...
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Decomposition of (2k+1)regular graphs containing special spanning 2kregular Cayley graphs into paths of length 2k+1
A P_ℓdecomposition of a graph G is a set of paths with ℓ edges in G tha...
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Proximity and Remoteness in Directed and Undirected Graphs
Let D be a strongly connected digraph. The average distance σ̅(v) of a v...
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The Dimension Spectrum Conjecture for Planar Lines
Let L_a,b be a line in the Euclidean plane with slope a and intercept b....
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Strong coloring 2regular graphs: Cycle restrictions and partial colorings
Let H be a graph with Δ(H) ≤ 2, and let G be obtained from H by gluing in vertexdisjoint copies of K_4. We prove that if H contains at most one odd cycle of length exceeding 3, or if H contains at most 3 triangles, then χ(G) ≤ 4. This proves the Strong Coloring Conjecture for such graphs H. For graphs H with Δ=2 that are not covered by our theorem, we prove an approximation result towards the conjecture.
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