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116
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DM
2010
14 years 12 months ago
2010
Let Mad(G) denote the maximum average degree (over all subgraphs) of G and let i(G) denote the injective chromatic number of G. We prove that if Mad(G) 5 2 , then i(G) + 1; sim...
105
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COMBINATORICS
2006
14 years 11 months ago
2006
A homomorphism from an oriented graph G to an oriented graph H is a mapping from the set of vertices of G to the set of vertices of H such that -----(u)(v) is an arc in H whenever...
CORR
2007
Springer
14 years 11 months ago
2007
Springer
A k-frugal colouring of a graph G is a proper colouring of the vertices of G such that no colour appears more than k times in the neighbourhood of a vertex. This type of colouring...
JCO
2007
14 years 11 months ago
2007
We consider the problem of orienting the edges of a graph so that the length of a longest path in the resulting digraph is minimum. As shown by Gallai, Roy and Vitaver, this edge ...
DM
1998
14 years 11 months ago
1998
We characterize the edge-signed graphs in which every 'significant' positive closed walk (or combination of walks) has even length, under seven different criteria for si...