Facial rainbow edge-coloring of simple 3-connected plane graphs
نویسندگان
چکیده
منابع مشابه
Facial non-repetitive edge-coloring of plane graphs
A sequence r1, r2, . . . , r2n such that ri = rn+i for all 1 ≤ i ≤ n, is called a repetition. A sequence S is called non-repetitive if no block (i.e. subsequence of consecutive terms of S) is a repetition. Let G be a graph whose edges are coloured. A trail is called non-repetitive if the sequence of colours of its edges is non-repetitive. If G is a plane graph, a facial non-repetitive edge-colo...
متن کاملEdge-coloring Vertex-weightings of Graphs
Let $G=(V(G),E(G))$ be a simple, finite and undirected graph of order $n$. A $k$-vertex weightings of a graph $G$ is a mapping $w: V(G) to {1, ldots, k}$. A $k$-vertex weighting induces an edge labeling $f_w: E(G) to N$ such that $f_w(uv)=w(u)+w(v)$. Such a labeling is called an {it edge-coloring k-vertex weightings} if $f_{w}(e)not= f_{w}(echr(chr(chr('39')39chr('39'))39chr(chr('39')39chr('39'...
متن کاملRainbow faces in edge-colored plane graphs
A face of an edge colored plane graph is called rainbow if all its edges receive distinct colors. The maximum number of colors used in an edge coloring of a connected plane graph G with no rainbow face is called the edge-rainbowness of G. In this paper we prove that the edge-rainbowness of G equals to the maximum number of edges of a connected bridge face factor H of G, where a bridge face fact...
متن کاملColoring intersection graphs of arc-connected sets in the plane
A family of sets in the plane is simple if the intersection of its any subfamily is arc-connected, and it is pierced by a line L if the intersection of its any member with L is a nonempty segment. It is proved that the intersection graphs of simple families of compact arc-connected sets in the plane pierced by a common line have chromatic number bounded by a function of their clique number.
متن کاملRainbow edge-coloring and rainbow domination
Let G be an edge-colored graph with n vertices. A rainbow subgraph is a subgraph whose edges have distinct colors. The rainbow edge-chromatic number of G, written χ̂′(G), is the minimum number of rainbow matchings needed to cover E(G). An edgecolored graph is t-tolerant if it contains no monochromatic star with t+1 edges. If G is t-tolerant, then χ̂′(G) < t(t+ 1)n lnn, and examples exist with χ̂′(...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Opuscula Mathematica
سال: 2020
ISSN: 1232-9274
DOI: 10.7494/opmath.2020.40.4.475