897 research outputs found
Injective colorings of graphs with low average degree
Let \mad(G) denote the maximum average degree (over all subgraphs) of
and let denote the injective chromatic number of . We prove that
if and \mad(G)<\frac{14}5, then . When
, we show that \mad(G)<\frac{36}{13} implies . In
contrast, we give a graph with , \mad(G)=\frac{36}{13}, and
.Comment: 15 pages, 3 figure
Injective colorings of sparse graphs
Let denote the maximum average degree (over all subgraphs) of
and let denote the injective chromatic number of . We prove that
if , then ; and if , then . Suppose that is a planar graph with
girth and . We prove that if , then
; similarly, if , then
.Comment: 10 page
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