Local edge coloring of graphs. Issue 1 (2nd January 2021) - Deepa, P.; Srinivasan, P.; Sundarakannan, M.
Abstract: Let G = ( V, E ) be a graph. A local edge coloring of G is a proper edge coloring c : E → N such that for each subset S of E ( G ) with 2 ≤ | S | ≤ 3, there exist edges e, f ∈ S such that | c ( e ) − c ( f ) | ≥ n s, where ns is the number of copies of P 3 in the edge induced subgraph 〈 S 〉 . The maximum color assigned by a local edge coloring c to an edge of G is called the value of c and is denoted by χ ℓ ′ ( c ) . The local edge chromatic number of G is χ ℓ ′ ( G ) = min { χ ℓ ′ ( c ) }, where the minimum is taken over all local edge colorings c of G . In this article, we derive bounds and many results based on local edge coloring.