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JGT
2006
14 years 11 months ago
2006
An edge-colored graph H is properly colored if no two adjacent edges of H have the same color. In 1997, J. Bang-Jensen and G. Gutin conjectured that an edgecolored complete graph ...
JGT
2010
14 years 10 months ago
2010
An edge-colored graph G is rainbow edge-connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection of a connected graph G, deno...
JGT
2010
14 years 10 months ago
2010
The crossing number, cr(G), of a graph G is the least number of crossing points in any drawing of G in the plane. According to the Crossing Lemma of Ajtai, Chv´atal, Newborn, Sze...
JGT
2010
14 years 10 months ago
2010
: We prove that the strong product G1 G2 of G1 and G2 is Z3-flow contractible if and only if G1 G2 is not T K2, where T is a tree (we call T K2 a K4-tree). It follows that G1 G2 ad...
JGT
2006
14 years 11 months ago
2006
Jeager et al introduced a concept of group connectivity as an generalization of nowhere zero flows and its dual concept group coloring, and conjectured that every 5-edge connected...