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- W3138749217 abstract "Given a graph $G$, a function $c:V(G)longrightarrow {1,ldots,k}$ with the property that $c(u)=c(v)=i$ implies that the distance between $u$ and $v$ is greater than $i$, is called a $k$-packing coloring of $G$. The smallest integer $k$ for which there exists a $k$-packing coloring of $G$ is called the packing chromatic number of $G$, and is denoted by $chi_rho$. Packing chromatic vertex-critical graphs are the graphs $G$ for which $chi_rho(G-x) < chi_rho(G)$ holds for every vertex $x$ of $G$. A graph $G$ is called a packing chromatic critical graph if for every proper subgraph $H$ of $G$, $chi_rho(H) < chi_rho(G)$. Both of the mentioned variations of critical graphs with respect to the packing chromatic number have already been studied. All packing chromatic (vertex-)critical graphs $G$ with $chi_rho(G)=3$ were characterized, while there were known only partial results for graphs $G$ with $chi_rho(G)=4$. In this paper, we provide characterizations of all packing chromatic vertex-critical graphs $G$ with $chi_rho(G)=4$ and all packing chromatic critical graphs $G$ with $chi_rho(G)=4$." @default.
- W3138749217 created "2021-03-29" @default.
- W3138749217 creator A5001781016 @default.
- W3138749217 date "2021-03-19" @default.
- W3138749217 modified "2023-09-27" @default.
- W3138749217 title "A characterization of $4$-$chi_rho$-(vertex-)critical graphs" @default.
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