A proper k-edge coloring f of graph G(V, E) is said to be a k:-adjacent strong edge coloring of graph G(V,E) iff every uv∈E(G) satisfy f[u]≠f/[v], where f[u] = {f(uw)|uw ∈E(G)} then f is called k-adjacent strong ed...A proper k-edge coloring f of graph G(V, E) is said to be a k:-adjacent strong edge coloring of graph G(V,E) iff every uv∈E(G) satisfy f[u]≠f/[v], where f[u] = {f(uw)|uw ∈E(G)} then f is called k-adjacent strong edge coloring of G, is abbreviated k-ASEC: and x'as(G) = min{k|k-ASEC of G} is called the adjacent strong edge chromatic number. In this paper, we study the x'as(G) of Halin graphs with △A(G)≥5.展开更多
A proper edge coloring of a graph G is said to be acyclic if there is no bicolored cycle in G.The acyclic edge chromatic number of G,denoted byχ′a(G),is the smallest number of colors in an acyclic edge coloring of G...A proper edge coloring of a graph G is said to be acyclic if there is no bicolored cycle in G.The acyclic edge chromatic number of G,denoted byχ′a(G),is the smallest number of colors in an acyclic edge coloring of G.Let G be a planar graph with maximum degree.In this paper,we show thatχ′a(G)+2,if G has no adjacent i-and j-cycles for any i,j∈{3,4,5},which implies a result of Hou,Liu and Wu(2012);andχ′a(G)+3,if G has no adjacent i-and j-cycles for any i,j∈{3,4,6}.展开更多
基金This work was partially supported by National Natural Science Foundation of China(No. 10471078)Doctoral Foundation of the Education committee of China(No. 2004042204)Supported by an NSERC grant Canada
基金Supported by NNSFC(19871036)"Qing Lan"talent funds of Lanzhou Railway Institute.
文摘A proper k-edge coloring f of graph G(V, E) is said to be a k:-adjacent strong edge coloring of graph G(V,E) iff every uv∈E(G) satisfy f[u]≠f/[v], where f[u] = {f(uw)|uw ∈E(G)} then f is called k-adjacent strong edge coloring of G, is abbreviated k-ASEC: and x'as(G) = min{k|k-ASEC of G} is called the adjacent strong edge chromatic number. In this paper, we study the x'as(G) of Halin graphs with △A(G)≥5.
基金supported by National Natural Science Foundation of China(Grant Nos.10931003 and 11171160)by Doctoral Fund of Ministry of Education of China(Grant No.10871011)
文摘A proper edge coloring of a graph G is said to be acyclic if there is no bicolored cycle in G.The acyclic edge chromatic number of G,denoted byχ′a(G),is the smallest number of colors in an acyclic edge coloring of G.Let G be a planar graph with maximum degree.In this paper,we show thatχ′a(G)+2,if G has no adjacent i-and j-cycles for any i,j∈{3,4,5},which implies a result of Hou,Liu and Wu(2012);andχ′a(G)+3,if G has no adjacent i-and j-cycles for any i,j∈{3,4,6}.
