A star edge coloring of a graph is a proper edge coloring without bichromatic paths and cycles of length four. In this paper we establish tight upper bounds for trees and subcubic outerplanar graphs, and derive an upper bound for outerplanar graphs.

Interaction among the scientific disciplines is of vital importance in modern science. Focusing on the case of Slovenia, we study the dynamics of interdisciplinary sciences from to . Our approach relies on quantifying the interdisciplinarity of research communities detected in the coauthorship network of Slovenian scientists over time. Examining the evolution of the community structure, we find that the frequency of interdisciplinary research is only proportional with the overall growth of the network. Although marginal improvements in favor of interdisciplinarity are inferable during the 70s and 80s, the overall trends during the past 20 years are constant and indicative of stalemate. We conclude that the flow of knowledge between different fields of research in Slovenia is in need of further stimulation.

An edge coloring of a graph G is said to be an odd edge coloring if for each vertex v of G and each color c, the vertex v uses the color c an odd number of times or does not use it at all. In [5], Pyber proved that 4 colors suffice for an odd edge coloring of any simple graph. Recently, some results on this type of colorings of (multi)graphs were successfully applied in solving a problem of facial parity edge coloring [3,2]. In this paper we present additional results, namely we prove that 6 colors suffice for an odd edge coloring of any loopless connected (multi)graph, provide examples showing that this upper bound is sharp and characterize the family of loopless connected (multi)graphs for which the bound 6 is achieved. We also pose several open problems.

A strong edge coloring of a graph is a proper edge coloring where the edges at distance at most two receive distinct colors. It is known that every planar graph with maximum degree ∆ has a strong edge coloring with at most 4 ∆ + 4 colors. We show that 3 ∆ + 6 colors suffice if the graph has girth 6, and 3 ∆ colors suffice if the girth is at least 7. Moreover, we show that cubic planar graphs with girth at least 6 can be strongly edge colored with at most 9 colors.