Bulky Subgraphs of the Hypercube

Hexagon-free subgraphs of hypercubes

✍ Marston Conder 📂 Article 📅 1993 🏛 John Wiley and Sons 🌐 English ⚖ 151 KB

On k-detour subgraphs of hypercubes

✍ Nana Arizumi; Peter Hamburger; Alexandr Kostochka 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 156 KB

## Abstract A spanning subgraph __G__ of a graph __H__ is a __k__‐__detour subgraph__ of __H__ if for each pair of vertices $x,y \in V(H)$, the distance, ${\rm dist}\_G(x,y)$, between __x__ and __y__ in __G__ exceeds that in __H__ by at most __k__. Such subgraphs sometimes also are called __additiv

Subgraphs of a hypercube containing no s

Subgraphs of a hypercube containing no small even cycles

✍ Fan R. K. Chung 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 490 KB

## Abstract We investigate several Ramsey‐Turán type problems for subgraphs of a hypercube. We obtain upper and lower bounds for the maximum number of edges in a subgraph of a hypercube containing no four‐cycles or more generally, no 2__k__‐cycles __C__~2k~. These extermal results imply, for exampl

The Terwilliger Algebra of the Hypercube

✍ Junie T Go 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 285 KB

Using the above equations, we find the irreducible T -modules. For each irreducible T -module W , we display two orthogonal bases, which we call the standard basis and the dual standard basis. We describe the action of A and A \* on each of these bases. We give the transition matrix from the standar

On the Achromatic Number of Hypercubes

✍ Yuval Roichman 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 96 KB

The achromatic number of a finite graph G, (G), is the maximum number of independent sets into which the vertex set may be partitioned, so that between any two parts there is at least one edge. For an m-dimensional hypercube P m 2 we prove that there exist constants 0<c 1 <c 2 , independent of m, su

The spanning subgraphs of eulerian graph

The spanning subgraphs of eulerian graphs

✍ F. T. Boesch; C. Suffel; R. Tindell 📂 Article 📅 1977 🏛 John Wiley and Sons 🌐 English ⚖ 312 KB

## Abstract It is shown that a connected graph __G__ spans an eulerian graph if and only if __G__ is not spanned by an odd complete bigraph __K__(2~m~ + 1, 2__n__ + 1). A disconnected graph spans an eulerian graph if and only if it is not the union of the trivial graph with a complete graph of odd