
On the chromatic numbers of signed triangular and hexagonal grids
A signed graph is a simple graph with two types of edges. Switching a ve...
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Extremality and Sharp Bounds for the kedgeconnectivity of Graphs
Boesch and Chen (SIAM J. Appl. Math., 1978) introduced the cutversion o...
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On relative clique number of colored mixed graphs
An (m, n)colored mixed graph is a graph having arcs of m different colo...
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Connectivity of orientations of 3edgeconnected graphs
We attempt to generalize a theorem of NashWilliams stating that a graph...
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Online Carpooling using Expander Decompositions
We consider the online carpooling problem: given n vertices, a sequence ...
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Representations of Sparse Distributed Networks: A LocalitySensitive Approach
In 1999, Brodal and Fagerberg (BF) gave an algorithm for maintaining a l...
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Bounds on Ramsey Games via Alterations
This note contains a refined alteration approach for constructing Hfree...
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The chromatic number of 2edgecolored and signed graphs of bounded maximum degree
A 2edgecolored graph or a signed graph is a simple graph with two types of edges. A homomorphism from a 2edgecolored graph G to a 2edgecolored graph H is a mapping φ: V(G) → V(H) that maps every edge in G to an edge of the same type in H. Switching a vertex v of a 2edgecolored or signed graph corresponds to changing the type of each edge incident to v. There is a homomorphism from the signed graph G to the signed graph H if after switching some subset of the vertices of G there is a 2edgecolored homomorphism from G to H. The chromatic number of a 2edgecolored (resp. signed) graph G is the order of a smallest 2edgecolored (resp. signed) graph H such that there is a homomorphism from G to H. The chromatic number of a class of graph is the maximum of the chromatic numbers of the graphs in the class. We study the chromatic numbers of 2edgecolored and signed graphs (connected and not necessarily connected) of a given bounded maximum degree. More precisely, we provide exact bounds for graphs of maximum degree 2. We then propose specific lower and upper bounds for graphs of maximum degree 3, 4, and 5. We finally propose general bounds for graphs of maximum degree k, for every k.
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