Facial Parity 9-Edge-Coloring of Outerplane Graphs

نویسندگان

Tomás Bálint

Július Czap

چکیده

A facial parity edge coloring of a 2-edge-connected plane graph is such an edge coloring in which no two face-adjacent edges (consecutive edges of a facial walk of some face) receive the same color, in addition, for each face f and each color c, either no edge or an odd number of edges incident with f is colored with c. It is known that any 2-edgeconnected plane graph has a facial parity edge coloring with at most 92 colors. In this paper we prove that any 2-edge-connected outerplane graph has a facial parity edge coloring with at most 15 colors. If a 2-edge-connected outerplane graph does not contain any inner edge, then 10 colors are sufficient. Moreover, this bound is tight.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Choosability, Edge Choosability, and Total Choosability of Outerplane Graphs

Let χl (G), χ ′ l (G), χ ′′ l (G), and 1(G) denote, respectively, the list chromatic number, the list chromatic index, the list total chromatic number, and the maximum degree of a non-trivial connected outerplane graph G. We prove the following results. (1) 2 ≤ χl (G) ≤ 3 and χl (G) = 2 if and only if G is bipartite with at most one cycle. (2) 1(G) ≤ χ ′ l (G) ≤ 1(G) + 1 and χ ′ l (G) = 1(G) + ...

متن کامل

Decompositions of plane graphs under parity constrains given by faces

An edge coloring of a plane graph G is facially proper if no two faceadjacent edges of G receive the same color. A facial (facially proper) parity edge coloring of a plane graph G is an (facially proper) edge coloring with the property that, for each color c and each face f of G, either an odd number of edges incident with f is colored with c, or color c does not occur on the edges of f . In th...

متن کامل

Edge-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 کامل

Optimal Parity Edge-Coloring of Complete Graphs

A parity walk in an edge-coloring of a graph is a walk along which each color is used an even number of times. Let p(G) be the least number of colors in an edge-coloring of G having no parity path (a parity edge-coloring). Let p̂(G) be the least number of colors in an edge-coloring of G having no open parity walk (a strong parity edge-coloring). Always p̂(G) ≥ p(G) ≥ χ′(G). We prove that p̂(Kn) = ...

متن کامل