All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1

Displaying 1 – 16 of 16

Showing per page

Large Degree Vertices in Longest Cycles of Graphs, I

Binlong Li, Liming Xiong, Jun Yin (2016)

Discussiones Mathematicae Graph Theory

In this paper, we consider the least integer d such that every longest cycle of a k-connected graph of order n (and of independent number α) contains all vertices of degree at least d.

Light paths with an odd number of vertices in polyhedral maps

Stanislav Jendroľ, Heinz-Jürgen Voss (2000)

Czechoslovak Mathematical Journal

Let P k be a path on k vertices. In an earlier paper we have proved that each polyhedral map G on any compact 2 -manifold 𝕄 with Euler characteristic χ ( 𝕄 ) ≤ 0 contains a path P k such that each vertex of this path has, in G , degree ≤ k 5 + 49 - 24 χ ( 𝕄 ) 2 . Moreover, this bound is attained for k = 1 or k ≥ 2 , k even. In this paper we prove that for each odd k ≥ 4 3 5 + 49 - 24 χ ( 𝕄 ) 2 + 1 , this bound is the best possible on infinitely many compact 2 -manifolds, but on infinitely many other compact 2 -manifolds the upper bound can be lowered to ( k - 1 3 ) 5 + 49 - 24 χ ( 𝕄 ) 2 .

Linear forests and ordered cycles

Guantao Chen, Ralph J. Faudree, Ronald J. Gould, Michael S. Jacobson, Linda Lesniak, Florian Pfender (2004)

Discussiones Mathematicae Graph Theory

A collection L = P ¹ ∪ P ² ∪ . . . ∪ P t (1 ≤ t ≤ k) of t disjoint paths, s of them being singletons with |V(L)| = k is called a (k,t,s)-linear forest. A graph G is (k,t,s)-ordered if for every (k,t,s)-linear forest L in G there exists a cycle C in G that contains the paths of L in the designated order as subpaths. If the cycle is also a hamiltonian cycle, then G is said to be (k,t,s)-ordered hamiltonian. We give sharp sum of degree conditions for nonadjacent vertices that imply a graph is (k,t,s)-ordered hamiltonian.

L-zero-divisor graphs of direct products of L-commutative rings

S. Ebrahimi Atani, M. Shajari Kohan (2011)

Discussiones Mathematicae - General Algebra and Applications

L-zero-divisor graphs of L-commutative rings have been introduced and studied in [5]. Here we consider L-zero-divisor graphs of a finite direct product of L-commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the L-ziro-divisor graph of a L-ring when extending to a finite direct product of L-commutative rings.

Currently displaying 1 – 16 of 16

Page 1