[PDF] Top 20 Hamiltonian Laceability in Line Graphs

... a Hamiltonian path between every pair of the distinct vertices in it at an odd ...a Hamiltonian-t-laceable if there exists a Hamiltonian path between every pair of the vertices u and v in G with the ... See full document

... a Hamiltonian path of the corresponding alphabet supergrid ...no Hamiltonian path, then the sewing track in it contains more than one path and these paths must be concatenated by jump ...supergrid ... See full document

... The Hamiltonian related problems on supergrid graphs can be applied to control the stitching trace of a computerized sewing machine as stated in ...the Hamiltonian path problem on grid graphs ... See full document

... of Hamiltonian graphs have been constructed and their various properties related to edge disjoint Hamiltonian cycles, vertex coloring, equal path partition and perfect matching have been discussed ... See full document

... In the previous sections, we show how to decompose the input graph to a collection of toroidal graphs. We can use Mohar’s algorithm to find an embedding for all those toroidal graphs in linear time. ... See full document

... All graphs considered in this paper are finite and undi- rected, without loops or multiple ...A Hamiltonian cycle in G is a sim- ple cycle in which each vertex of G appears exactly ...A Hamiltonian ... See full document

... the Hamiltonian connectivity of L-shaped supergrid graphs, we can seek the end vertices of Hamiltonian paths in the corresponding L-shaped supergrid graphs so that the total length of jump ... See full document

... These graphs were introduced by Lovász in his celebrated proof of Kneser’s conjecture ...exciting line of research [Bár78, Gre02, Zie02, Mat04] and gave rise to the nowadays flourishing field of topological ... See full document

... are Hamiltonian connected except few trivial ...or Hamiltonian paths between two distinct vertices of shaped supergrid ...supergrid graphs. We can see from the structures of alphabet supergrid ... See full document

... a line graph if there exists a graph H such that G = L ( H ...of line graphs is probably a forbidden subgraph characterization due to Beineke ...A Hamiltonian cycle in a graph G is a cycle ... See full document

... is Hamiltonian, if it contains a Hamilton cycle. A graph G is Hamiltonian laceable if there is a u-v Hamiltonian path for all pair of vertices u and v where d(u,v) is ...is Hamiltonian - k - ... See full document

... is Hamiltonian laceable if there exists a Hamiltonian path between every pair of distinct vertices at an odd distance in ...is Hamiltonian-t-laceable( t * -laceable) if there exists a ... See full document

... of line graphs and that of line graphs of subdivision graphs of well known classes of graphs have been subject to study of molecular graph theory by many ...the line ... See full document

... 3–regular graphs exist with arbitrary girth, the construction can only produce bridge ...These graphs are, perhaps, uninteresting as they can be detected in polynomial ...3–regular graphs, ... See full document

... 3.8 Theorem: If G is a graph containing only one edge that is |EG| = 1 then the graph Q2G contains unique triangle.. is a triangle in Q2G containing the edge e..[r] ... See full document

... in graphs by creating a set of low degree vertices and then using them to create a set of disjoint paths that each have at least one of the vertices from the ... See full document

... Spectral invariants have been used to study a variety of properties of graphs. See, for instance, [9] [5] [6] [7]. In this note, we will present sufficient conditions which are based on the spectral radius for ... See full document

... 2-step Hamiltonian labeling for each odd cycle and the ring worm with odd cycle corre- spond to a vertex labeling that induces an edge labeling f + such that the edge labels form a sequence of consecutive ... See full document

... While the chracterization problem has been solved for line signed graph (i.e., signed graph S for which their exists a signed graph H such that L ( H ) ≅ S as in [5]), the same remains to be solved for the × ... See full document

... the line graph, shown in Section 5, also gives a new method for con- structing non-representable graphs when starting with an arbitrary graph (excluding cycles, paths and the claw graph of ...presentable ... See full document