WebAn embedding ˙of a graph G= (V;E) in a surface is an injective ... coloring ’of a graph Gis a mapping from V(G) to a set of colors Csuch that ’(u) 6= ’(v) whenever uv2E(G). ... Theorem 2 ([2, 17]). Let Gbe a triangle-free planar graph and Hbe a graph such that G= H hfor some edge hof H. Then His 3-colorable. Theorem 3 ([17]). Let Gbe a ... WebDec 1, 2024 · An injective k -edge coloring of a graph G= (V (G),E (G)) is a k -edge coloring \varphi of G such that \varphi (e_1)\ne \varphi (e_3) for any three consecutive edges e_1,e_2 and e_3 of a path or a 3-cycle. The injective edge chromatic index of G, denoted by \chi _i' (G), is the minimum k such that G has an injective k -edge coloring.
Injective edge-coloring of graphs with given maximum …
WebMar 1, 2024 · An injective edge-coloring of graph G is an edge-coloring φ such that φ ( e 1 ) ≠ φ ( e 3 ) for any three consecutive edges e 1, e 2 and e 3 of a path or a 3-cycle. Note that … WebMar 31, 2024 · An injective edge-coloring of graph G is an edge coloring φ such that φ (e 1) ≠ φ (e 3) for any three consecutive edges e 1, e 2 and e 3 of a path or a 3-cycle. In other … scoring knife是什么
Injective Edge-Coloring of Graphs with Small Weight
WebJul 15, 2024 · An injective coloring of a graph is a vertex coloring such that any pair of vertices having a common neighbor receives distinct colors. Panda and Priyamvada [ 12 ] proved complexity results for some subclasses of bipartite graphs, which can be re-interpreted as results on exact square coloring. WebA vi-simultaneous proper k-coloring of a graph G is a coloring of all vertices and incidences of the graph in which any two adjacent or incident elements in the set V(G)∪I(G) receive distinct colors, where I(G) is the set of incidences of G.The vi-simultaneous chromatic number, denoted by χ vi (G), is the smallest integer k such that G has a vi-simultaneous … WebAbstract A k -injective edge coloring of a graph G is a coloring f: E ( G) → C = { 1, 2, 3, …, k }, such that if e 1, e 2 and e 3 are consecutive edges in G, then f ( e 1) ≠ f ( e 3). χ i ′ ( G) = … scoring knife lowe\u0027s