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A {em strong $k$-edge-coloring} of a graph $G$ is a mapping from $E(G)$ to ${1,2,ldots,k}$ such that every two adjacent edges or two edges adjacent to the same edge receive distinct colors. The {em strong chromatic index} $chi_s(G)$ of a graph $G$ is the smallest integer $k$ such that $G$ admits a strong $k$-edge-coloring. We give bounds on $chi_s(G)$ in terms of the maximum degree $Delta(G)$ of a graph $G$. when $G$ is sparse, namely, when $G$ is $2$-degenerate or when the maximum average degree ${rm Mad}(G)$ is small. We prove that the strong chromatic index of each $2$-degenerate graph $G$ is at most $5Delta(G) +1$. Furthermore, we show that for a graph $G$, if ${rm Mad}(G)< 8/3$ and $Delta(G)geq 9$, then $chi_s(G)leq 3Delta(G) -3$ (the bound $3Delta(G) -3$ is sharp) and if ${rm Mad}(G)<3$ and $Delta(G)geq 7$, then $chi_s(G)leq 3Delta(G)$ (the restriction ${rm Mad}(G)<3$ is sharp).
A strong edge-coloring of a graph $G$ is an edge-coloring such that any two edges on a path of length three receive distinct colors. We denote the strong chromatic index by $chi_{s}(G)$ which is the minimum number of colors that allow a strong edge-c
Given a digraph $D$ with $m $ arcs, a bijection $tau: A(D)rightarrow {1, 2, ldots, m}$ is an antimagic labeling of $D$ if no two vertices in $D$ have the same vertex-sum, where the vertex-sum of a vertex $u $ in $D$ under $tau$ is the sum of labels o
Let $G$ be a simple graph with maximum degree $Delta(G)$. A subgraph $H$ of $G$ is overfull if $|E(H)|>Delta(G)lfloor |V(H)|/2 rfloor$. Chetwynd and Hilton in 1985 conjectured that a graph $G$ with $Delta(G)>|V(G)|/3$ has chromatic index $Delta(G)$ i
Given a simple graph $G$, denote by $Delta(G)$, $delta(G)$, and $chi(G)$ the maximum degree, the minimum degree, and the chromatic index of $G$, respectively. We say $G$ is emph{$Delta$-critical} if $chi(G)=Delta(G)+1$ and $chi(H)le Delta(G)$ for eve
A $k$-improper edge coloring of a graph $G$ is a mapping $alpha:E(G)longrightarrow mathbb{N}$ such that at most $k$ edges of $G$ with a common endpoint have the same color. An improper edge coloring of a graph $G$ is called an improper interval edge