Contractible Cycles in Graphs with Girth at Least 5

نویسندگان

چکیده

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Planar graphs with girth at least 5 are (3, 5)-colorable

A graph is (d1, . . . , dr )-colorable if its vertex set can be partitioned into r sets V1, . . . , Vr where themaximum degree of the graph induced by Vi is at most di for each i ∈ {1, . . . , r}. Let Gg denote the class of planar graphs with minimum cycle length at least g . We focus on graphs in G5 since for any d1 and d2, Montassier and Ochem constructed graphs in G4 that are not (d1, d2)-co...

متن کامل

Altitude of regular graphs with girth at least five

The altitude of a graph G is the largest integer k such that for each linear ordering f of its edges, G has a (simple) path P of length k for which f increases along the edge sequence of P . We determine a necessary and sufficient condition for cubic graphs with girth at least five to have altitude three and show that for r 4, r-regular graphs with girth at least five have altitude at least fou...

متن کامل

A new upper bound for the spectral radius of graphs with girth at least 5

Let G be a simple connected graph with V (G) = {v1, v2, . . . , vn} and girth at least 5. Let be the maximum degree of G. In this paper, we present a new sharp upper bound for the spectral radius of G as follows: ρ(G) −1 + √ 4n+ 4 − 3 2 . Moreover, equality holds if and only if G∼=C5. © 2005 Elsevier Inc. All rights reserved. AMS classification: 05C50; 15A18

متن کامل

The distinguishing chromatic number of bipartite graphs of girth at least six

The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling   with $d$ labels  that is preserved only by a trivial automorphism. The distinguishing chromatic number $chi_{D}(G)$ of $G$ is defined similarly, where, in addition, $f$ is assumed to be a proper labeling. We prove that if $G$ is a bipartite graph of girth at least six with the maximum ...

متن کامل

Excluding Minors In Nonplanar Graphs Of Girth At Least Five

A graph is quasi 4-connected if it is simple, 3-connected, has at least five vertices, and for every partition (A, B, C) of V (G) either |C| ≥ 4, or G has an edge with one end in A and the other end in B, or one of A,B has at most one vertex. We show that any quasi 4-connected nonplanar graph with minimum degree at least three and no cycle of length less than five has a minor isomorphic to P− 1...

متن کامل

ذخیره 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: Journal of Combinatorial Theory, Series B

سال: 1998

ISSN: 0095-8956

DOI: 10.1006/jctb.1998.1844