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Subgraphs of a hypercube containing no small even cycles
Author(s) -
Chung Fan R. K.
Publication year - 1992
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190160311
Subject(s) - hypercube , combinatorics , mathematics , integer (computer science) , cube (algebra) , enhanced data rates for gsm evolution , discrete mathematics , computer science , telecommunications , programming language
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 example, the following Ramsey theorems for hypercubes: A hypercube can always be edge‐partitioned into four subgraphs, each of which contains no six‐cycle. However, for any integer t , if the n ‐cube is edge‐partitioned into t sub‐graphs, then one of the subgraphs must contain an edight‐cycle, provided only than n is sufficiently large (depending only on t ).