O jednom algoritme z oblasti ohodnotených grafov
O jednom extremálním problému pro grafy s
O jednom zobecnění vnějškově rovinných grafů
O konstrukcích orientovaných grafů
O kubických grafech
O minimálních grafech, obsahujících daných bodů
O perfektních a kvaziperfektních grafech
O studentském semináři z teorie grafů na Matematicko-fyzikální fakultě KU
O vnoření dichotomického stromu do krychle
Observability of a graph
Octonion multiplication and Heawood’s map
In this note, the octonion multiplication table is recovered from a regular tesselation of the equilateral two timensional torus by seven hexagons, also known as Heawood’s map.
OD-characterization of almost simple groups related to
In the present paper, we classify groups with the same order and degree pattern as an almost simple group related to the projective special linear simple group . As a consequence of this result we can give a positive answer to a conjecture of W. J. Shi and J. X. Bi, for all almost simple groups related to except . Also, we prove that if is an almost simple group related to except and is a finite group such that and , then .
Odd and residue domination numbers of a graph
Let G = (V,E) be a simple, undirected graph. A set of vertices D is called an odd dominating set if |N[v] ∩ D| ≡ 1 (mod 2) for every vertex v ∈ V(G). The minimum cardinality of an odd dominating set is called the odd domination number of G, denoted by γ₁(G). In this paper, several algorithmic and structural results are presented on this parameter for grids, complements of powers of cycles, and other graph classes as well as for more general forms of "residue" domination.
Odd cutsets and the hard-core model on
We consider the hard-core lattice gas model on and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds , the model exhibits multiple hard-core measures, thus improving the previous bound of given by Galvin and Kahn. At the heart of our approach lies the study of a certain class of edge cutsets in , the so-called odd cutsets, that appear naturally as the boundary between different phases in the hard-core model. We provide a refined combinatorial...
Odd cycles and a class of facets of the axial 3-index assignment polytope
Odd graphs
Odd mean labeling of the graphs and
Odd-vertex-degree trees maximizing Wiener index
Offensive alliances in graphs
A set S is an offensive alliance if for every vertex v in its boundary N(S)- S it holds that the majority of vertices in v's closed neighbourhood are in S. The offensive alliance number is the minimum cardinality of an offensive alliance. In this paper we explore the bounds on the offensive alliance and the strong offensive alliance numbers (where a strict majority is required). In particular, we show that the offensive alliance number is at most 2/3 the order and the strong offensive alliance number...
Old and new generalizations of line graphs.