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- W3206253709 abstract "If $S=(s_1,s_2,ldots)$ is a non-decreasing sequence of positive integers, then the $S$-packing $k$-coloring of a graph $G$ is a mapping $c: V(G)rightarrow[k]$ such that if $c(u)=c(v)=i$ for $uneq vin V(G)$, then $d_G(u,v)>s_i$. The $S$-packing chromatic number of $G$ is the smallest integer $k$ such that $G$ admits an $S$-packing $k$-coloring. A graph $G$ is $chi_S$-critical if $chi_S(G-u) < chi_S(G)$ for each $uin V(G)$. If $G$ is $chi_S$-critical and $chi_S(G) = k$, then $G$ is $k$-$chi_S$-vertex-critical. In this paper, $4$-$chi_S$-vertex-critical graphs are characterized for sequences $S = (1,s_2, s_3, ldots)$ with $s_2 ge 3$. There are $28$ sporadic examples and two infinite families of such graphs." @default.
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- W3206253709 date "2021-10-12" @default.
- W3206253709 modified "2023-09-27" @default.
- W3206253709 title "A characterization of 4-$chi_S$-vertex-critical graphs for $Ssucceq (1,3,3,3,ldots)$" @default.
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