Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A vertex coloring of a graph G is called injective if any two vertices with a common neighbor receive distinct colors. A graph G is injectively k -choosable if any list L of admissible colors on V ( G ) of size k allows an injective coloring ź such that ź ( v ) ź L ( v ) whenever v ź V ( G ) . The least k for which G is injectively k -choosable is denoted by ź i l ( G ) . ,  show that if G is a planar graph with girth g ź 6 , then ź i l ( G ) ź Δ + 3 .
['Hong-Yu Chen', 'Jian-Liang Wu']
I am writing a research paper on a idea List injective coloring of planar graphs with girth g ≥ 6
[{"from": "human", "value": "I am writing a research paper on a idea List injective coloring of planar graphs with girth g \u2265 6"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A vertex coloring of a graph G is called injective if any two vertices with a common neighbor receive distinct colors. A graph G is injectively k -choosable if any list L of admissible colors on V ( G ) of size k allows an injective coloring \u017a such that \u017a ( v ) \u017a L ( v ) whenever v \u017a V ( G ) . The least k for which G is injectively k -choosable is denoted by \u017a i l ( G ) . ,  show that if G is a planar graph with girth g \u017a 6 , then \u017a i l ( G ) \u017a \u0394 + 3 ."}]