An injective k-edge coloring of a graph G is k-edge coloringκof G such thatκ(e1)≠κ(e3)for any three consecutive edges ei,e2 and e3 of a path or a triangle.The injective chromatic index of G,denoted by x'i(G),i...An injective k-edge coloring of a graph G is k-edge coloringκof G such thatκ(e1)≠κ(e3)for any three consecutive edges ei,e2 and e3 of a path or a triangle.The injective chromatic index of G,denoted by x'i(G),is the smallest integer k such that G has an injective k-edge coloring.In this paper,we prove that x'i(G)≤9 if G is a planar graph with maximum degreeΔ≤4,girth g≥6 and without intersecting 6-cycles.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.12071265,12001481)the Natural Science Foundation of Shandong Province(Grant No.ZR2021MA103)the Youth Innovation Team Project of Shandong Province Universities(Grant No.2024KJG078).
文摘An injective k-edge coloring of a graph G is k-edge coloringκof G such thatκ(e1)≠κ(e3)for any three consecutive edges ei,e2 and e3 of a path or a triangle.The injective chromatic index of G,denoted by x'i(G),is the smallest integer k such that G has an injective k-edge coloring.In this paper,we prove that x'i(G)≤9 if G is a planar graph with maximum degreeΔ≤4,girth g≥6 and without intersecting 6-cycles.
