Cycles and paths in multigraphs

نویسندگان

  • Roger B. Eggleton
  • Derek A. Holton
  • Charles H. C. Little
چکیده

We consider cycles and paths in multigraphic realizations of a degree sequence Q. in particular we show that there exists a realization of d in which no cycle has order greater than three and no path has length greater than four. In addition we show which orders of cycles and which lengths of paths exist in some realization of d.

برای دانلود رایگان 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

Alternating cycles and paths in edge-coloured multigraphs: A survey

A path or cycle in an edge-coloured multigraph is called alternating if its successive edges differ in colour. We survey results of both theoretical and algorithmic character concerning alternating cycles and paths in edge-coloured multigraphs. We also show useful connections between the theory of paths and cycles in bipartite digraphs and the theory of alternating paths and cycles in edge-colo...

متن کامل

Cycles and paths in edge-colored graphs with given degrees

Sufficient degree conditions for the existence of properly edge-colored cycles and paths in edge-colored graphs, multigraphs and random graphs are inverstigated. In particular, we prove that an edgecolored multigraph of order n on at least three colors and with minimum colored degree greater than or equal to d 2 e has properly edge-colored cycles of all possible lengths, including hamiltonian c...

متن کامل

Some maximum multigraphs and adge/vertex distance colourings

Shannon–Vizing–type problems concerning the upper bound for a distance chromatic index of multigraphs G in terms of the maximum degree ∆(G) are studied. Conjectures generalizing those related to the strong chromatic index are presented. The chromatic d–index and chromatic d–number of paths, cycles, trees and some hypercubes are determined. Among hypercubes, however, the exact order of their gro...

متن کامل

Properly Coloured Cycles and Paths: Results and Open Problems

In this paper, we consider a number of results and six conjectures on properly coloured (PC) paths and cycles in edge-coloured multigraphs. We overview some known results and prove new ones. In particular, we consider a family of transformations of an edge-coloured multigraph G into an ordinary graph that allow us to check the existence of PC cycles and PC (s, t)-paths in G and, if they exist, ...

متن کامل

Characterization of signed paths and cycles admitting minus dominating function

If G = (V, E, σ) is a finite signed graph, a function f : V → {−1, 0, 1} is a minusdominating function (MDF) of G if f(u) +summation over all vertices v∈N(u) of σ(uv)f(v) ≥ 1 for all u ∈ V . In this paper we characterize signed paths and cycles admitting an MDF.

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

عنوان ژورنال:
  • Australasian J. Combinatorics

دوره 5  شماره 

صفحات  -

تاریخ انتشار 1992